A362080 a(n) = [x^n] 1/(1 - x*(1+x)^n)^n.

1, 1, 7, 55, 571, 7026, 98925, 1562219, 27214867, 516646333, 10589130223, 232574622116, 5440521381816, 134859301929873, 3527034780915985, 96965997588549555, 2793286163779275779, 84076751617833902070, 2637677096916448507104

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..449

Formula

a(n) = Sum_{k=0..n} (-1)^k * binomial(-n,k) * binomial(n*k,n-k) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n*k,n-k).

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n*k, n-k));

Crossrefs

Main diagonal of A362078.

Main diagonal of A362079.

Sequence in context: A094905 A178922 A306046 * A355409 A112243 A083836

Adjacent sequences: A362077 A362078 A362079 * A362081 A362082 A362083

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2023

Status

approved