A378555 a(n) = Sum_{k=0..n} 9^(n-k) * binomial(n+k-1,k) * binomial(k/3,n-k).

1, 1, 9, 19, 305, 156, 13233, -23988, 688113, -2863070, 41085704, -246536784, 2696513885, -19410931916, 187672944300, -1481383572516, 13522625165601, -111877103550195, 994511499413664, -8430550720540365, 74061353032540020, -636000265949289978

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = [x^n] 1/(1 - x*(1 + 9*x)^(1/3))^n.

Mathematica

a[n_]:=SeriesCoefficient[1/(1 - x*(1 + 9*x)^(1/3))^n, {x, 0, n}]; Array[a, 22, 0] (* Stefano Spezia, Nov 30 2024 *)

Prog

(PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(n+k-1, k)*binomial(k/3, n-k));

Crossrefs

Cf. A213684, A378554.

Cf. A372126.

Sequence in context: A335782 A041677 A153316 * A041160 A248305 A089565

Adjacent sequences: A378552 A378553 A378554 * A378560 A378561 A378565

Keyword

sign,new

Author

Seiichi Manyama, Nov 30 2024

Status

approved