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