A372464 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x+x^2) )^(2*n).

1, 4, 32, 286, 2688, 26004, 256334, 2560352, 25824768, 262447684, 2683152032, 27565067600, 284330359950, 2942808943572, 30546407611136, 317867390671536, 3314979452815360, 34637849797078380, 362544825234198020, 3800439733237986800, 39893311092729794688

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n+k-1,k) * binomial(5*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)^2 * (1-x+x^2)^2 ). See A368975.

Prog

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

Crossrefs

Cf. A368975, A372460.

Sequence in context: A319183 A199566 A370160 * A366663 A110901 A295538

Adjacent sequences: A372461 A372462 A372463 * A372465 A372466 A372467

Keyword

nonn

Author

Seiichi Manyama, May 01 2024

Status

approved