A382544 Expansion of 1/(1 - x/(1 - 9*x)^(1/3))^3.

1, 3, 15, 100, 753, 6006, 49456, 415422, 3536802, 30404161, 263271639, 2292524970, 20052238465, 176029542285, 1549916592645, 13681091072620, 121020187476717, 1072477163769417, 9519299301332377, 84609930915003882, 752947626436806021, 6707715814093174588

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = Sum_{k=0..n} 9^(n-k) * binomial(k+2,2) * binomial(n-2*k/3-1,n-k).

Mathematica

Table[Sum[9^(n-k)*Binomial[k+2, 2]* Binomial [n-2*k/3-1, n-k], {k, 0, n}], {n, 0, 25}] (* Vincenzo Librandi, Mar 31 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(k+2, 2)*binomial(n-2*k/3-1, n-k));
(Magma) R<x> := PowerSeriesRing(Rationals(), 25); f := x / (1 - 9*x)^(1/3); G := 1 / (1 - f)^3; Coefficients(G); // Vincenzo Librandi, Mar 31 2025

Crossrefs

Cf. A362206, A382543.

Sequence in context: A135883 A372157 A387982 * A381906 A147664 A384680

Adjacent sequences: A382541 A382542 A382543 * A382545 A382546 A382547

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 31 2025

Status

approved