A391080 Expansion of g^2/(1 - x^2*g^3), where g = 1+x*g^4 is the g.f. of A002293.

1, 2, 10, 57, 371, 2602, 19196, 146813, 1153554, 9255781, 75519859, 624675625, 5226355365, 44149963427, 376053050411, 3226085416241, 27849752177424, 241749252280205, 2108824279848025, 18476616002606832, 162525066740933049, 1434731262290652282

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} (3*k+2) * binomial(4*n-5*k+2,n-2*k)/(4*n-5*k+2).

Mathematica

Table[Sum[ (3*k+2)*Binomial[4* n-5*k+2, n-2*k]/(4*n-5*k+2), {k, 0, Floor[n/2]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 29 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (3*k+2)*binomial(4*n-5*k+2, n-2*k)/(4*n-5*k+2));
(Magma) [&+[(3*k+2)*Binomial(4*n-5*k+2, n-2*k)/(4*n-5*k+2): k in [0..Floor(n/2)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 29 2025

Crossrefs

Cf. A389112, A390147, A391082, A391084.

Cf. A002293.

Sequence in context: A371770 A390520 A369487 * A248403 A278095 A075870

Adjacent sequences: A391077 A391078 A391079 * A391081 A391082 A391083

Keyword

nonn

Author

Seiichi Manyama, Nov 27 2025

Status

approved