A372178 E.g.f. A(x) satisfies A(x) = exp( 2 * x * A(x)^(1/2) * (1 + x * A(x)) ).

1, 2, 12, 122, 1800, 35002, 848236, 24664362, 837602352, 32558200370, 1426118691924, 69522324440098, 3733960438696648, 219101400537409002, 13946923555466389884, 957297896801470079258, 70483467144263313405024, 5541471459106022647303522

Offset

0,2

Links

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

Formula

E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A363355.

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

Crossrefs

Cf. A363355, A372164, A372179.

Sequence in context: A058349 A375897 A013469 * A246738 A039933 A364397

Adjacent sequences: A372175 A372176 A372177 * A372179 A372180 A372181

Keyword

nonn

Author

Seiichi Manyama, Apr 21 2024

Status

approved