A380665 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-x/(1 - x)) ).

1, 3, 31, 586, 16401, 612336, 28678231, 1618268688, 106946168769, 8105456425600, 693228400344591, 66055574392722432, 6940237183385667409, 797165049089377683456, 99381018789002592800775, 13365207839280075801020416, 1928719845703457066672384769, 297293268794967068206087176192

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Index entries for reversions of series

Formula

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

a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(3*n+1,n-k)/k!.

Prog

(PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(3*n+1, n-k)/k!);

Crossrefs

Cf. A052873, A380663.

Cf. A377832.

Sequence in context: A273378 A266487 A229258 * A319896 A370260 A222895

Adjacent sequences: A380659 A380663 A380664 * A380666 A380667 A380671

Keyword

nonn,new

Author

Seiichi Manyama, Jan 30 2025

Status

approved