A230317 E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * Product_{k=1..n} A(k*x).

1, 1, 3, 19, 215, 4016, 119092, 5503205, 393154477, 43298176708, 7340865004766, 1913028475033699, 764596866776205619, 467416620805272150858, 435773832975324764799712, 617753035395626539657324801, 1327738980050724547857227605753, 4314831625390935798178255342966024

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..76

Example

G.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 215*x^4/4! + 4016*x^5/5! +...
where
A(x) = 1 + x*A(x) + x^2*A(x)*A(2*x)/2! + x^3*A(x)*A(2*x)*A(3*x)/3! + x^4*A(x)*A(2*x)*A(3*x)*A(4*x)/4! + x^5*A(x)*A(2*x)*A(3*x)*A(4*x)*A(5*x)/5! +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m/m!*prod(k=1, m, subst(A, x, k*x+x*O(x^n))))); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A230321, A178087.

Sequence in context: A000275 A058165 A074707 * A135749 A005647 A158876

Adjacent sequences: A230314 A230315 A230316 * A230318 A230319 A230320

Keyword

nonn

Author

Paul D. Hanna, Oct 15 2013

Status

approved