A177340 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(n(3n-1)/2).

1, 1, 2, 8, 41, 244, 1605, 11350, 84949, 666221, 5439193, 46026398, 402493943, 3630344538, 33731558974, 322633261521, 3175444787672, 32156075992687, 335029146470043, 3591545445240954, 39615629451300230, 449583342724740800

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

Let A = g.f. A(x), then A satisfies:

A = Sum_{n>=0} x^n*A^n*Product_{k=1..n} (1-x*A^(6k-5))/(1-x*A^(6k-2)) due to a q-series identity.

G.f. A(x) satisfies: A(x) = B(x/A(x)) and A(x*B(x)) = B(x) where B(x) = g.f. of A177341.

Example

G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 41*x^4 + 244*x^5 + 1605*x^6 +...
A(x) = 1 + x*A(x) + x^2*A(x)^5 + x^3*A(x)^12 + x^4*A(x)^22 +...

Prog

(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*A^(j*(3*j-1)/2)+x*O(x^n))); polcoeff(A, n)}

Crossrefs

Cf. A177341.

Sequence in context: A333093 A217362 A294084 * A067119 A093935 A099240

Adjacent sequences: A177337 A177338 A177339 * A177341 A177342 A177343

Keyword

nonn

Author

Paul D. Hanna, May 06 2010

Status

approved