A370988 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x) - 1)) ).
1, 0, 2, 3, 76, 425, 10326, 119077, 3158968, 57929265, 1740086290, 44066266541, 1512768107940, 48660920528233, 1905202422005806, 73878129769929045, 3275941116578461936, 147981592692778718561, 7366814796135956094378, 378666415166758834858237
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x)-1)))/x)) -
PARI
a(n) = sum(k=0, n\2, (n+k)!*stirling(n-k, k, 2)/(n-k)!)/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (n+k)! * Stirling2(n-k,k)/(n-k)!.