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A371342
E.g.f. satisfies A(x) = log(1 + x/(1 - A(x))).
3
0, 1, 1, 5, 38, 404, 5514, 91916, 1810080, 41119704, 1058505600, 30450551592, 968121778128, 33709242522864, 1275738359407680, 52141501470591360, 2288907292892799744, 107405692000948859904, 5365016291068305805440, 284225212617080543066880
OFFSET
0,4
FORMULA
E.g.f.: Series_Reversion( (1 - x) * (exp(x) - 1) ).
a(n) = Sum_{k=1..n} (n+k-2)!/(n-1)! * Stirling1(n,k).
a(n) ~ LambertW(1)^n * n^(n-1) / (sqrt(1 + LambertW(1)) * exp(n) * (1 - LambertW(1))^(2*n-1)). - Vaclav Kotesovec, Mar 19 2024
MATHEMATICA
Table[Sum[(n+k-2)! / (n-1)! * StirlingS1[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 19 2024 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)*(exp(x)-1)))))
(PARI) a(n) = sum(k=1, n, (n+k-2)!/(n-1)!*stirling(n, k, 1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 19 2024
STATUS
approved