A378554 a(n) = Sum_{k=0..n} 4^(n-k) * binomial(n+k-1,k) * binomial(k/2,n-k).

1, 1, 7, 28, 171, 846, 4942, 26580, 153363, 856900, 4939682, 28140476, 162676878, 936947116, 5436375532, 31526252208, 183571246659, 1069552636950, 6247183319938, 36524006501180, 213899020967786, 1253905101529080, 7359775341696180, 43237184121401400

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Formula

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

Mathematica

a[n_]:=SeriesCoefficient[1/(1 - x*(1 + 4*x)^(1/2))^n, {x, 0, n}]; Array[a, 24, 0] (* Stefano Spezia, Nov 30 2024 *)

Prog

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

Crossrefs

Cf. A213684, A378555.

Cf. A372125.

Sequence in context: A304520 A335759 A224663 * A203296 A355155 A058822

Adjacent sequences: A378551 A378552 A378553 * A378555 A378556 A378557

Keyword

nonn

Author

Seiichi Manyama, Nov 30 2024

Status

approved