A371326 -id:A371326 - cp's OEIS frontend

A370922 E.g.f. satisfies A(x) = log(1 + x/(1 - A(x)))/(1 - A(x)).

0, 1, 3, 29, 444, 9454, 257822, 8576504, 336770592, 15246592440, 781883091672, 44797478362680, 2836034500712256, 196601715537070752, 14811696896760459264, 1205008924460733794688, 105284627507520312994560, 9832559605580777568425856

Offset: 0

Seiichi Manyama, Mar 19 2024

nonn

Index entries for reversions of series

Cf. A371326, A371342.

a(n) = sum(k=1, n, (n+2*k-2)!/(n+k-1)!*stirling(n, k, 1));

a(n) = Sum_{k=1..n} (n+2*k-2)!/(n+k-1)! * Stirling1(n,k).

E.g.f.: Series_Reversion( (1 - x) * (exp(x * (1 - x)) - 1) ). - Seiichi Manyama, Sep 09 2024

A371342 E.g.f. satisfies A(x) = log(1 + x/(1 - A(x))).

Original entry on oeis.org

0, 1, 1, 5, 38, 404, 5514, 91916, 1810080, 41119704, 1058505600, 30450551592, 968121778128, 33709242522864, 1275738359407680, 52141501470591360, 2288907292892799744, 107405692000948859904, 5365016291068305805440, 284225212617080543066880

Offset: 0

Seiichi Manyama, Mar 19 2024

nonn

Index entries for reversions of series

Cf. A370922, A371326.

Cf. A052842, A052892.

Table[Sum[(n+k-2)! / (n-1)! * StirlingS1[n,k], {k,1,n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 19 2024 *)

my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(serreverse((1-x)*(exp(x)-1)))))

a(n) = sum(k=1, n, (n+k-2)!/(n-1)!*stirling(n, k, 1));

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

cp's OEIS Frontend

A370922 E.g.f. satisfies A(x) = log(1 + x/(1 - A(x)))/(1 - A(x)).

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A371342 E.g.f. satisfies A(x) = log(1 + x/(1 - A(x))).

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