A354316 Expansion of e.g.f. 1/(1 + x/3 * log(1 - 3 * x)).
1, 0, 2, 9, 96, 1170, 18324, 340200, 7360128, 181476288, 5024611440, 154319988240, 5206240427904, 191372822989920, 7612497915813504, 325791049256094240, 14925809593280332800, 728828735500650355200, 37786217117138333005824
Offset: 0
Keywords
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[1/(1+x/3 Log[1-3x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 06 2023 *) -
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x/3*log(1-3*x)))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!*sum(j=2, i, 3^(j-2)/(j-1)*v[i-j+1]/(i-j)!)); v;
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PARI
a(n) = n!*sum(k=0, n\2, 3^(n-2*k)*k!*abs(stirling(n-k, k, 1))/(n-k)!);
Formula
a(0) = 1; a(n) = n! * Sum_{k=2..n} 3^(k-2)/(k-1) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/2)} 3^(n-2*k) * k! * |Stirling1(n-k,k)|/(n-k)!.