A131351 G.f.: A(x) = 1 + Sum_{n>=1} x^n*[ Product_{k=1..n} F_k(x) ] where F_n(x) = 1 + x*F_n(x)^n.

1, 1, 2, 4, 9, 24, 77, 295, 1329, 6924, 41030, 272271, 1996406, 16000511, 138953665, 1298206570, 12969761907, 137846434950, 1551712558368, 18429620298121, 230175973108212, 3014142623764514, 41275488455847862, 589698136493691293

Offset

0,3

Links

Table of n, a(n) for n=0..23.

Example

A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 24*x^5 + 77*x^6 + 295*x^7 +...
A(x) = 1 + x*F_1(x) + x^2*F_1(x)*F_2(x) + x^3*F_1(x)*F_2(x)*F_3(x) +...
where F_n(x) = Sum_{k>=0} C(n*k,k)/((n-1)*k + 1)*x^k:
F_1(x) = 1/(1-x);
F_2(x) = 1 + x + 2x^2 + 5x^3 + 14x^4 + 42x^5 + +... (A000108);
F_3(x) = 1 + x + 3x^2 + 12x^3 + 55x^4 + 273x^5 + ...(A001764);
F_4(x) = 1 + x + 4x^2 + 22x^3 + 140x^4 + 969x^5 +...(A002293); ...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=0, n, A=1+x*A* Ser(vector(n+1, i, binomial((n-k+1)*(i-1), i-1)/((n-k)*(i-1)+1)))); polcoeff(A, n) }

Crossrefs

Sequence in context: A093542 A301927 A000667 * A091352 A135934 A343032

Adjacent sequences: A131348 A131349 A131350 * A131352 A131353 A131354

Keyword

nonn

Author

Paul D. Hanna, Jul 03 2007

Status

approved