How this calculator works
Every row begins and ends with 1. Interior entries are the sum of the two entries directly above. These entries are binomial coefficients, which also count ways to choose k items from n. Exact integer arithmetic preserves large coefficients. Rows are presented as coefficient strings so even a wide row remains readable in a scrollable table.
Formula
Row n contains C(n,k), k = 0,...,n. C(n,0)=1 and C(n,k)=C(n,k-1)(n-k+1)/k. Row sum = 2^n.
Worked example
Row 4 is 1, 4, 6, 4, 1 and sums to 16. Row 5 is 1, 5, 10, 10, 5, 1 and sums to 32.
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Frequently asked questions
Why is the top called row zero?
Its only coefficient is C(0,0) = 1. This indexing matches the exponent in the binomial theorem.
What are the coefficients used for?
They appear in (a+b)^n, combination counts and binomial probability formulas.
Are large values rounded?
No. Coefficients and row sums are calculated with exact integers and displayed as text.