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A370988
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x) - 1)) ).
10
1, 0, 2, 3, 76, 425, 10326, 119077, 3158968, 57929265, 1740086290, 44066266541, 1512768107940, 48660920528233, 1905202422005806, 73878129769929045, 3275941116578461936, 147981592692778718561, 7366814796135956094378, 378666415166758834858237
OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (n+k)! * Stirling2(n-k,k)/(n-k)!.
PROG
(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);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 06 2024
STATUS
approved