A367488 Expansion of e.g.f. 1/(4 - 3*exp(x))^x.

1, 0, 6, 36, 444, 6540, 119520, 2593164, 65233392, 1867289868, 59939612040, 2132540249532, 83293357351248, 3543242182036284, 163062595422642552, 8071964230348189260, 427682380939864204224, 24149065480351703398572, 1447640087400503974386504

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = 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])); v;

Crossrefs

Cf. A032033, A367472, A367473.

Cf. A354413, A367486.

Cf. A367490.

Sequence in context: A201540 A195229 A366654 * A339300 A296389 A077290

Adjacent sequences: A367485 A367486 A367487 * A367489 A367490 A367491

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2023

Status

approved