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A381982

E.g.f. A(x) satisfies A(x) = exp(x) * C(x*A(x)), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.

1, 2, 11, 139, 2829, 78981, 2802163, 120667667, 6113752025, 356342305465, 23488872131871, 1727770084512495, 140302645206245701, 12466960491079733237, 1203253101643330233707, 125351056198801059896491, 14019427299278115378992049, 1675439381194882102492648305

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OFFSET

0,2

LINKS

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

FORMULA

Let F(x) be the e.g.f. of A364983. F(x) = C(x*A(x)) = exp( 1/2 * Sum_{k>=1} binomial(2*k,k) * (x*A(x))^k/k ).

a(n) = n! * Sum_{k=0..n} (k+1)^(n-k) * A001764(k)/(n-k)!.

PROG

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

CROSSREFS

Cf. A349640, A381983.