A218216 G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k)^4 * x^k*(1-x)^(n-k).

1, 1, 1, 15, 65, 175, 1155, 7229, 31081, 162755, 1018195, 5448645, 28879019, 171229541, 991796825, 5540516759, 32232757569, 190448140543, 1105001828111, 6463178610505, 38380301015595, 227218808375165, 1344777832158545, 8022879439995215, 47988823484272835

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Example

G.f.: A(x) = 1 + x + x^2 + 15*x^3 + 65*x^4 + 175*x^5 + 1155*x^6 + 7229*x^7 +...
where
A(x) = 1 +
x*((1-x) + x) +
x^2*((1-x)^2 + 2^4*x*(1-x) + x^2) +
x^3*((1-x)^3 + 3^4*x*(1-x)^2 + 3^4*x^2*(1-x) + x^3) +
x^4*((1-x)^4 + 4^4*x*(1-x)^3 + 6^4*x^2*(1-x)^2 + 4^4*x^3*(1-x) + x^4) +
x^5*((1-x)^5 + 5^4*x*(1-x)^4 + 10^4*x^2*(1-x)^3 + 10^4*x^3*(1-x)^2 + 5^4*x^4*(1-x) + x^5) +...

Prog

(PARI) {a(n)=polcoeff(sum(m=0, n+1, x^m*sum(k=0, m, binomial(m, k)^4*x^k*(1-x)^(m-k) + x*O(x^n))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A217615, A217421.

Sequence in context: A147858 A364401 A005917 * A027455 A152729 A055268

Adjacent sequences: A218213 A218214 A218215 * A218217 A218218 A218219

Keyword

nonn

Author

Paul D. Hanna, Oct 23 2012

Status

approved