A368233 Expansion of e.g.f. 1/(1 - 2*x - log(1 + x)).
1, 3, 17, 146, 1668, 23834, 408614, 8173248, 186836952, 4804906656, 137297982672, 4315550336448, 147977856835440, 5496919791479856, 219900767818247952, 9425346313165808064, 430919959212816772608, 20932680398362302305664
Offset: 0
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[1/(1-2x-Log[1+x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Sep 02 2025 *) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*i*v[i]+sum(j=1, i, (-1)^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = 2*n*a(n-1) + Sum_{k=1..n} (-1)^(k-1) * (k-1)! * binomial(n,k) * a(n-k).