A367485 Expansion of e.g.f. 1/(3 - 2*exp(x))^(x/2).

1, 0, 2, 9, 72, 735, 9300, 140511, 2469600, 49509711, 1115030220, 27871094823, 765622756800, 22925878253031, 743201185847484, 25930679953675815, 968847417413563200, 38593990513290611967, 1632776110278839747532, 73111823927074777887111

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} A367489(k) * binomial(n-1,k-1) * a(n-k).

Mathematica

With[{nn=20}, CoefficientList[Series[1/(3-2Exp[x])^(x/2), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 29 2024 *)

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, 2^k*(k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])/2); v;

Crossrefs

Cf. A354412, A367487.

Cf. A367486, A367489.

Sequence in context: A258114 A349583 A370889 * A133941 A240956 A038035

Adjacent sequences: A367482 A367483 A367484 * A367486 A367487 A367488

Keyword

nonn

Author

Seiichi Manyama, Nov 19 2023

Status

approved