A391102 Expansion of g^3/(1 - x^2*g), where g = 1+x*g^4 is the g.f. of A002293.

1, 3, 16, 95, 635, 4534, 33890, 261765, 2072641, 16732801, 137213748, 1139738646, 9569342309, 81082064798, 692433744780, 5953828761669, 51500965421571, 447852196503417, 3912938946491980, 34332723663216311, 302391399344255051, 2672583238541562604

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..floor(n/2)} (k+3) * binomial(4*n-7*k+3,n-2*k)/(4*n-7*k+3).

Mathematica

Table[Sum[ (k+3)*Binomial[4* n-7*k+3, n-2*k]/(4*n-7*k+3), {k, 0, Floor[n/2]}], {n, 0, 26}] (* Vincenzo Librandi, Nov 30 2025 *)

Prog

(PARI) a(n) = sum(k=0, n\2, (k+3)*binomial(4*n-7*k+3, n-2*k)/(4*n-7*k+3));
(Magma) [&+[(k+3)*Binomial(4*n-7*k+3, n-2*k)/(4*n-7*k+3): k in [0..Floor(n/2)]] : n in [0..40] ]; // Vincenzo Librandi, Nov 30 2025

Crossrefs

Cf. A002293, A389112, A390280.

Sequence in context: A137644 A114174 A181067 * A006347 A000270 A157051

Adjacent sequences: A391099 A391100 A391101 * A391103 A391104 A391105

Keyword

nonn

Author

Seiichi Manyama, Nov 28 2025

Status

approved