A391172 Expansion of g^2/(1 - x*g)^3, where g = 1+x*g^3 is the g.f. of A001764.

1, 5, 22, 100, 481, 2436, 12860, 70134, 392390, 2240568, 13006942, 76543610, 455611562, 2738301975, 16594871736, 101296441536, 622232097195, 3843500042366, 23858833802820, 148762390102942, 931250036847218, 5850644655163475, 36877623062423404, 233141721974594250

Offset

0,2

Links

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

Formula

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

Mathematica

Table[Sum[(k+2)*Binomial[k+2, 2]*Binomial[3*n-2*k+2, n-k]/(3*n-2*k+2), {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Dec 02 2025  *)

Prog

(PARI) a(n) = sum(k=0, n, (k+2)*binomial(k+2, 2)*binomial(3*n-2*k+2, n-k)/(3*n-2*k+2));
(Magma) [&+[(k+2)*Binomial(k+2, 2)*Binomial(3*n-2*k+2, n-k)/(3*n-2*k+2): k in [0..n]] : n in [0..30] ]; // Vincenzo Librandi, Dec 02 2025

Crossrefs

Cf. A006013, A390719, A391171, A391173.

Cf. A001764.

Sequence in context: A123347 A087439 A033452 * A346772 A295519 A179602

Adjacent sequences: A391169 A391170 A391171 * A391173 A391174 A391175

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2025

Status

approved