A389115 Expansion of g^3/(1 + x*g)^2, where g = 1+x*g^2 is the g.f. of A000108.

1, 1, 4, 11, 35, 113, 376, 1276, 4402, 15390, 54408, 194169, 698567, 2530937, 9226160, 33815432, 124538318, 460644494, 1710476504, 6373775030, 23826843614, 89331823706, 335823046544, 1265571538136, 4780273605460, 18094046107408, 68623099425856, 260734318876725

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = Sum_{k=0..n} (-1)^k * (k+1) * (k+3) * binomial(2*n-k+3,n-k)/(2*n-k+3).

a(n) = (1/(n+3)) * Sum_{k=0..n} (-1)^k * (k+1) * (k+3) * binomial(2*n-k+2,n-k).

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*(k+1)*(k+3)*binomial(2*n-k+3, n-k)/(2*n-k+3));

Crossrefs

Cf. A065601, A114495, A391408.

Cf. A104629, A294527.

Cf. A000108, A000344, A391405.

Sequence in context: A197626 A349185 A358826 * A212910 A339034 A114248

Adjacent sequences: A389112 A389113 A389114 * A389116 A389117 A389118

Keyword

nonn

Author

Seiichi Manyama, Dec 08 2025

Status

approved