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A177340
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G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(n(3n-1)/2).
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1
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1, 1, 2, 8, 41, 244, 1605, 11350, 84949, 666221, 5439193, 46026398, 402493943, 3630344538, 33731558974, 322633261521, 3175444787672, 32156075992687, 335029146470043, 3591545445240954, 39615629451300230, 449583342724740800
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OFFSET
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0,3
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LINKS
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FORMULA
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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.
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EXAMPLE
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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 +...
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PROG
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(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)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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