A367487 Expansion of e.g.f. 1/(4 - 3*exp(x))^(x/2).

1, 0, 3, 18, 195, 2730, 47745, 1001742, 24523401, 686190258, 21601161015, 755533274826, 29066119327179, 1219715093642838, 55441103383640793, 2713468284508412430, 142269924567096468177, 7955396173559375208426, 472576083221524737100311

Offset: 0

Author

Seiichi Manyama, Nov 19 2023

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..372

Crossrefs

Cf. A354412, A367485.

Cf. A367490.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[1/(4-3Exp[x])^(x/2),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 23 2025 *)

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*sum(k=1, j-1, 3^k*(k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])/2); v;

Formula

a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} A367490(k) * binomial(n-1,k-1) * a(n-k).