A372460 Coefficient of x^n in the expansion of 1 / ( (1-x) * (1-x-x^2) )^(2*n).

1, 4, 40, 442, 5136, 61424, 748462, 9240480, 115194720, 1446820588, 18279806600, 232071505120, 2958062657550, 37831613904036, 485233557808704, 6239148779539472, 80397210629541696, 1037970502613332320, 13423439565585274180, 173859642721737225552

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..floor(n/2)} 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 A368967.

Prog

(PARI) a(n, s=2, t=2, u=2) = 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. A368967, A372233, A372464.

Sequence in context: A221588 A114468 A264112 * A304447 A370444 A002705

Adjacent sequences: A372457 A372458 A372459 * A372461 A372462 A372463

Keyword

nonn

Author

Seiichi Manyama, May 01 2024

Status

approved