A377831 -id:A377831 - cp's OEIS frontend

A380718 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2) / (1 - x*A(x)).

1, 2, 17, 277, 6809, 225381, 9408745, 474835159, 28128322801, 1913917635433, 147124118481641, 12610993501595523, 1192699876840875529, 123380247466574450509, 13858619936380747514953, 1679795510876270598645631, 218541202774350975212752865, 30376105717226232363041309265

Offset: 0

Seiichi Manyama, Jan 30 2025

nonn

Cf. A380663, A380719.

Cf. A377831.

a(n) = n!*sum(k=0, n, (n+k+1)^(k-1)*binomial(2*n, n-k)/k!);

a(n) = n! * Sum_{k=0..n} (n+k+1)^(k-1) * binomial(2*n,n-k)/k!.

A380673 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x) * exp(-x * (1 - x)) ).

Original entry on oeis.org

1, 2, 11, 106, 1501, 28416, 677839, 19566128, 663801849, 25897000960, 1142424023731, 56232973813248, 3055417111781269, 181644488496644096, 11728204122824976375, 817281148114199197696, 61136484485752079320561, 4886365932210442324672512, 415573028022035962921316059

Offset: 0

Seiichi Manyama, Jan 30 2025

nonn

Index entries for reversions of series

Cf. A377831, A380663, A380664.

Cf. A277184.

a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(2*n-2*k, n-k)/k!);

E.g.f. A(x) satisfies A(x) = exp(x * A(x) * (1 - x*A(x)))/(1 - x*A(x)).
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n-2*k,n-k)/k!.
a(n) = A277184(n+1)/(n+1).

cp's OEIS Frontend

A380718 E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2) / (1 - x*A(x)).

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