A367852 Expansion of e.g.f. 1/(1 - x + log(1 - 3*x)/3).
1, 2, 11, 102, 1320, 21804, 436986, 10283580, 277697304, 8458929792, 286825214592, 10712216384352, 436859348261904, 19313926491051360, 920053448561989296, 46977842202096405024, 2559387620091962391552, 148187802162935002975488
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 3^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 3^(k-1) * (k-1)! * binomial(n,k) * a(n-k).