A378551 a(n) = Sum_{k=0..n} 4^k * binomial(n/2+k-1,k) * binomial(n-1,n-k).

1, 2, 20, 206, 2200, 24062, 267500, 3009050, 34150000, 390265190, 4484762500, 51771831146, 599921125000, 6974108163778, 81297715937500, 949957147566086, 11123368187500000, 130487420114543110, 1533247106445312500, 18042303960492212810, 212590835968046875000

Offset

0,2

Links

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

Formula

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

Mathematica

a[n_]:=SeriesCoefficient[ 1/(1 - 4*x/(1-x))^(n/2), {x, 0, n}]; Array[a, 21, 0] (* Stefano Spezia, Nov 30 2024 *)

Prog

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

Crossrefs

Cf. A002002, A378552.

Cf. A372109.

Sequence in context: A037624 A077327 A173499 * A067636 A226301 A000906

Adjacent sequences: A378548 A378549 A378550 * A378552 A378553 A378554

Keyword

nonn,new

Author

Seiichi Manyama, Nov 30 2024

Status

approved