A382649 Expansion of 1/(1 - x*(1 + 4*x)^(3/2))^2.

1, 2, 15, 52, 213, 834, 3043, 11576, 41601, 152458, 544039, 1950132, 6895773, 24403302, 85542339, 300101048, 1044436937, 3639851814, 12594713911, 43660404108, 150357976533, 518991977194, 1780132570723, 6122965091976, 20928650616113, 71779065646510, 244590689773839

Offset

0,2

Comments

a(82) is negative.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..600

Formula

a(n) = Sum_{k=0..n} 4^(n-k) * (k+1) * binomial(3*k/2,n-k).

Mathematica

Table[Sum[4^(n-k)* (k+1)* Binomial[3*k/2, n-k], {k, 0, n}], {n, 0, 28}] (* Vincenzo Librandi, May 13 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(3*k/2, n-k));
(Magma) R<x>:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(3/2))^2)); // Vincenzo Librandi, May 13 2025

Crossrefs

Cf. A382536, A382650.

Sequence in context: A248543 A248544 A344819 * A015520 A098520 A216333

Adjacent sequences: A382646 A382647 A382648 * A382650 A382651 A382652

Keyword

sign,easy

Author

Seiichi Manyama, Apr 02 2025

Status

approved