A368467 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n,k) * binomial(4*n,n-k).

1, 2, 2, -16, -126, -498, -880, 3432, 37762, 175916, 411502, -710752, -12482928, -66911830, -190616760, 70959984, 4208145282, 26042918836, 86794308524, 50521487200, -1397839172626, -10176550581570, -38838971577536, -51156092490048, 443929768322704

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = [x^n] ( (1-x)^2 * (1+x)^4 )^n.

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)^4) ). See A369190.

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k * binomial(2*n, k)*binomial(4*n, n-k));

Crossrefs

Cf. A234839, A370106.

Cf. A369190.

Sequence in context: A062282 A230990 A217977 * A012319 A012520 A012323

Adjacent sequences: A368464 A368465 A368466 * A368468 A368469 A368470

Keyword

sign

Author

Seiichi Manyama, Feb 10 2024

Status

approved