A159594 G.f.: A(x) = x*exp( Sum_{n>=1} [ D^n A(x) ]^n/n ), where differential operator D = x*d/dx.

1, 1, 3, 16, 125, 1301, 17070, 272976, 5218727, 118508219, 3224104875, 108226321884, 4740041705554, 291705715765328, 26728599026539162, 3688459631229579912, 751246585455211054713, 208348432365596381718906

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Formula

G.f.: A(x) = x*exp( Sum_{n>=1} [ Sum_{k>=1} k^n*a(k)*x^k ]^n/n ) where A(x) = Sum_{k>=1} a(k)*x^k.

Example

G.f.: A(x) = x + x^2 + 3*x^3 + 16*x^4 + 125*x^5 + 1301*x^6 +...
A(x) = x*exp( Sum_{n>=1} [x + 2^n*a(2)*x^2 + 3^n*a(3)*x^3 +...]^n/n ).
D^n A(x) = x + 2^n*x^2 + 3^n*3*x^3 + 4^n*16*x^4 + 5^n*125*x^5 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=x*exp(sum(m=1, n, sum(k=1, n, k^m*x^k*polcoeff(A, k)+x*O(x^n))^m/m))); polcoeff(A, n)}

Crossrefs

Sequence in context: A000951 A000272 A246527 * A246525 A193242 A247591

Adjacent sequences: A159591 A159592 A159593 * A159595 A159596 A159597

Keyword

nonn

Author

Paul D. Hanna, May 03 2009

Status

approved