A391097 Expansion of g/(1 - x^2*g^2), where g = 1+x*g^4 is the g.f. of A002293.

1, 1, 5, 25, 156, 1065, 7727, 58416, 455097, 3627727, 29445912, 242538753, 2022089118, 17031178367, 144698018623, 1238616098931, 10672094457215, 92482500970487, 805532278017869, 7048262626115086, 61923519049531805, 546048967970474367, 4831275866003151802

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{k=0..floor(n/2)} (2*k+1) * binomial(4*n-6*k+1,n-2*k)/(4*n-6*k+1).

Maple

Table[Sum[ (2*k+1)*Binomial[4* n-6*k+1, n-2*k]/(4*n-6*k+1), {k, 0, Floor[n/2]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (2*k+1)*binomial(4*n-6*k+1, n-2*k)/(4*n-6*k+1));
(Magma) [&+[(2*k+1)*Binomial(4*n-6*k+1, n-2*k)/(4*n-6*k+1): k in [0..Floor(n/2)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A109963, A390280, A391099, A391104.

Cf. A002293.

Sequence in context: A121112 A090014 A249475 * A179324 A097145 A392538

Adjacent sequences: A391094 A391095 A391096 * A391098 A391099 A391100

Keyword

nonn

Author

Seiichi Manyama, Nov 28 2025

Status

approved