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

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Prog

(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;

Crossrefs

Cf. A354412, A367485.

Cf. A367490.

Sequence in context: A308134 A160707 A330764 * A377545 A277355 A135077

Adjacent sequences: A367484 A367485 A367486 * A367488 A367489 A367490

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2023

Status

approved