A375899 E.g.f. satisfies A(x) = 1 / (1 + log(1 - x * A(x)^(1/2)))^2.
1, 2, 12, 124, 1846, 36128, 879252, 25637680, 872159952, 33933231696, 1486845891696, 72473120203680, 3890486148311040, 228103117063828992, 14504759878784601600, 994346460412330358016, 73107707092779695687040, 5738844073788385570644480
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x*(1+log(1-x)))/x)^2)) -
PARI
a(n) = 2*sum(k=0, n, (n+k+1)!*abs(stirling(n, k, 1)))/(n+2)!;
Formula
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052802.
E.g.f.: A(x) = ( (1/x) * Series_Reversion(x * (1 + log(1-x))) )^2.
a(n) = (2/(n+2)!) * Sum_{k=0..n} (n+k+1)! * |Stirling1(n,k)|.