A391408 Expansion of g^5/(1 + x*g)^2, where g = 1+x*g^2 is the g.f. of A000108.

1, 3, 11, 38, 133, 468, 1660, 5932, 21346, 77301, 281545, 1030778, 3791597, 14006456, 51941576, 193301120, 721697246, 2702472854, 10147300982, 38197179692, 144119279906, 544941540968, 2064663329656, 7837201508508, 29801069731228, 113504582390857, 432973857932389

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = Sum_{k=0..n} (-1)^k * (k+1) * (k+5) * binomial(2*n-k+5,n-k)/(2*n-k+5).

a(n) = (1/(n+5)) * Sum_{k=0..n} (-1)^k * (k+1) * (k+5) * binomial(2*n-k+4,n-k).

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(k+1)*(k+5)*binomial(2*n-k+5, n-k)/(2*n-k+5));

Crossrefs

Cf. A065601, A114495, A389115.

Cf. A000108.

Sequence in context: A026943 A307571 A381760 * A384705 A047096 A149060

Adjacent sequences: A391405 A391406 A391407 * A391409 A391410 A391411

Keyword

nonn

Author

Seiichi Manyama, Dec 08 2025

Status

approved