A161605 E.g.f. satisfies: A(x) = exp(x*exp(x*A(x)^3)).

1, 1, 3, 28, 365, 6496, 147127, 4033408, 130058777, 4822981120, 202225551371, 9460961327104, 488602134968389, 27609977350868992, 1694576741234926655, 112258296102497099776, 7983577042683934226993, 606688287932557859356672

Offset

0,3

Comments

More generally, if G(x) = exp(x*exp(x*G(x)^p)),

where G(x)^m = Sum_{n>=0} g(n,m)*x^n/n!,

then g(n,m) = Sum_{k=0..n} C(n,k) * m*(p*(n-k) + m)^(k-1) * k^(n-k).

Links

G. C. Greubel, Table of n, a(n) for n = 0..355

Formula

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

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 28*x^3/3! + 365*x^4/4! +...

Mathematica

Flatten[{1, Table[Sum[Binomial[n, k]*(3*(n - k) + 1)^(k - 1)*k^(n - k), {k, 0, n}], {n, 1, 50}]}] (* G. C. Greubel, Nov 18 2017 *)

Prog

(PARI) {a(n)=sum(k=0, n, binomial(n, k)*(3*(n-k)+1)^(k-1)*k^(n-k))}
(PARI) {a(n)=local(A=1+x); for(i=0, n, A=exp(x*exp(x*A^3+O(x^n)))); n!*polcoeff(A, n, x)}

Crossrefs

Cf. A161552, A161567.

Sequence in context: A212032 A352383 A151423 * A048954 A086569 A264639

Adjacent sequences: A161602 A161603 A161604 * A161606 A161607 A161608

Keyword

nonn

Author

Paul D. Hanna, Jun 14 2009

Status

approved