A372458 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^2)^2 )^n.

1, 3, 25, 225, 2129, 20723, 205471, 2063890, 20931585, 213864939, 2198044805, 22699471171, 235354244255, 2448409104820, 25544033624414, 267158874185420, 2800191197529633, 29405702263792875, 309320021637262225, 3258658594126096867, 34376186445159365709

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

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

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x * (1-x) * (1-x-x^2)^2 ). See A368965.

Prog

(PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((t+u+1)*n-(s-1)*k-1, n-s*k));

Crossrefs

Cf. A368965, A372233.

Sequence in context: A024217 A199679 A118726 * A066221 A370280 A367786

Adjacent sequences: A372455 A372456 A372457 * A372459 A372460 A372461

Keyword

nonn

Author

Seiichi Manyama, May 01 2024

Status

approved