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 A177340 G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^(n(3n-1)/2). 1
 1, 1, 2, 8, 41, 244, 1605, 11350, 84949, 666221, 5439193, 46026398, 402493943, 3630344538, 33731558974, 322633261521, 3175444787672, 32156075992687, 335029146470043, 3591545445240954, 39615629451300230, 449583342724740800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS 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: A020083 A217362 A294084 * A067119 A093935 A099240 Adjacent sequences:  A177337 A177338 A177339 * A177341 A177342 A177343 KEYWORD nonn AUTHOR Paul D. Hanna, May 06 2010 STATUS approved

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Last modified October 16 20:55 EDT 2019. Contains 328103 sequences. (Running on oeis4.)