A382541 Expansion of 1/(1 - x/(1 - 4*x)^(3/2))^2.

1, 2, 15, 100, 645, 4098, 25795, 161256, 1002513, 6203434, 38230951, 234774948, 1437193101, 8773022374, 53416562787, 324488659784, 1967025910873, 11901070329414, 71878009609591, 433411746865948, 2609477469570885, 15689257525890666, 94208451895149123

Offset

0,2

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(n+k/2-1,n-k).

D-finite with recurrence (-n+1)*a(n) +2*(8*n-13)*a(n-1) +(-95*n+217)*a(n-2) +2*(126*n-359)*a(n-3) +128*(-2*n+7)*a(n-4)=0. - R. J. Mathar, Apr 02 2025

Mathematica

Table[Sum[(4)^(n-k)* (k+1)* Binomial[n+k/2-1, n-k], {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, May 12 2025 *)

Prog

(PARI) a(n) = sum(k=0, n, 4^(n-k)*(k+1)*binomial(n+k/2-1, n-k));
(Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( 1/(1 - x/(1-4*x)^(3/2))^2)); // Vincenzo Librandi, May 12 2025

Crossrefs

Cf. A382514, A382542.

Cf. A382539.

Sequence in context: A376922 A258390 A378001 * A027080 A208347 A396556

Adjacent sequences: A382538 A382539 A382540 * A382542 A382543 A382544

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 31 2025

Status

approved