The number of bonds between carbon and oxygen atoms in major product of the following reaction is________.
`CH_(3)overset(OH)overset(|)(CHCH_(2)CH_(2)NH_(2)) overset("ethyl formate (1 equiv)")underset("triethylam in e")to`

Explanation

To solve the question regarding the number of bonds between carbon and oxygen atoms in the major product of the given reaction, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Reactants**: The reactants are 3-aminobutane (CH₃CH(CH₂)CH₂NH₂) and ethyl formate (HCOOC₂H₅).

2. **Determine the Reaction Mechanism**: In this reaction, the carbonyl carbon of ethyl formate will be attacked by the nitrogen atom of the amine (3-aminobutane) because nitrogen is less electronegative than oxygen and has a lone pair available for donation.

3. **Formation of the Intermediate**: When nitrogen attacks the carbonyl carbon, the carbonyl double bond (C=O) breaks. This results in the formation of a tetrahedral intermediate where the nitrogen is bonded to the carbon, and the oxygen carries a negative charge (O⁻).

4. **Rearrangement and Elimination**: The tetrahedral intermediate will rearrange, and the negatively charged oxygen will facilitate the departure of the ethyl group (C₂H₅O⁻), resulting in the formation of a new carbon-nitrogen bond.

5. **Final Product Structure**: After the rearrangement, the major product is a compound where the nitrogen is bonded to the carbon chain, and the carbonyl carbon is now bonded to a hydroxyl group (OH) and a carbonyl oxygen (C=O).

6. **Count the Bonds**: In the final product, we have:
- One carbon-oxygen double bond (C=O) which is a pi bond.
- One carbon-oxygen single bond (C-O) which is a sigma bond.
- Another carbon-oxygen single bond (C-O) from the hydroxyl group (OH).

Therefore, the total number of bonds between carbon and oxygen in the product is:
- 1 sigma bond (from C-O in OH)
- 1 sigma bond (from C-O in C=O)
- 1 pi bond (from C=O)

This gives us a total of **3 bonds** (2 sigma bonds and 1 pi bond) between carbon and oxygen.

### Final Answer:
The number of bonds between carbon and oxygen atoms in the major product of the reaction is **3**.