A355787 E.g.f. satisfies A(x) = (1 + 2*x)^(A(x)/2).
1, 1, 1, 6, 17, 220, 939, 20930, 107393, 3823416, 20382195, 1147905462, 5519388225, 515034742404, 1817577994491, 323878306632330, 481078381979649, 272556878473903344, -355395800536648605, 296393140746445749246, -1420979986049970526335
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-log(1+2*x)/2)))) -
PARI
a(n) = sum(k=0, n, 2^(n-k)*(k+1)^(k-1)*stirling(n, k, 1));
Formula
E.g.f.: exp( -LambertW(-log(1+2*x)/2) ).
a(n) = Sum_{k=0..n} 2^(n-k) * (k+1)^(k-1) * Stirling1(n,k).