A372164 E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(5/2) * (1 + x * A(x)) ).

1, 2, 28, 746, 30344, 1668762, 116000044, 9760665434, 964821252528, 109605653026802, 14072453189095124, 2015280776336738418, 318501367837803765640, 55067060355743834423690, 10339257411931121356190652, 2095051036885575920328492938, 455698493422117961626699815776

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A372182.

If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) * (1 + x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(s*k,n-k)/k!.

Prog

(PARI) a(n, r=2, s=1, t=5, u=2) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(s*k, n-k)/k!);

Crossrefs

Cf. A371574, A372165, A372182.

Sequence in context: A151332 A098631 A089836 * A372165 A090249 A264411

Adjacent sequences: A372161 A372162 A372163 * A372165 A372166 A372167

Keyword

nonn

Author

Seiichi Manyama, Apr 21 2024

Status

approved