A382515 Expansion of 1/(1 - x/(1 - 4*x)^(5/2)).

1, 1, 11, 91, 691, 5101, 37323, 272405, 1987047, 14493479, 105718071, 771148119, 5625136651, 41032826127, 299316769887, 2183389173811, 15926906427179, 116180104751925, 847485191674867, 6182049517420133, 45095462188117951, 328952511222499589, 2399570809473795931

Offset: 0

Author

Seiichi Manyama, Mar 30 2025

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A026671, A382514.

Cf. A002802.

Programs

Mathematica

Table[Sum[4^(n-k)*Binomial[n+3*k/2-1,n-k],{k,0,n}],{n,0,25}] (* Vincenzo Librandi, Mar 30 2025 *)

PARI

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

Formula

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

D-finite with recurrence (-n+1)*a(n) +2*(12*n-19)*a(n-1) +(-239*n+519)*a(n-2) +2*(638*n-1751)*a(n-3) +1280*(-3*n+10)*a(n-4) +512*(12*n-47)*a(n-5) +2048*(-2*n+9)*a(n-6)=0. - R. J. Mathar, Mar 31 2025