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

Author

Seiichi Manyama, Apr 02 2025

Keywords

• sign
• easy

Comments

a(82) is negative.

Links

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

Crossrefs

Cf. A382536, A382650.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 28); Coefficients(R!( 1/(1 - x*(1 + 4*x)^(3/2))^2)); // Vincenzo Librandi, May 13 2025

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 *)

PARI

a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(3*k/2, n-k));

Formula

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