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 A218295 G.f. satisfies: A(x) = 1 + Sum_{n>=1} 2*x^n * A(x)^(3*n^2). 1
 1, 2, 14, 158, 2274, 37410, 670670, 12786622, 255519106, 5302716866, 113586849614, 2501007496542, 56446396937186, 1303401799574242, 30756416720161422, 741216834445478270, 18240706372460480002, 458484823574294544770, 11776969626284389958030 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Given g.f. A(x), then Q = A(-x^2) satisfies: Q = (1-x)*Sum_{n>=0} x^n*Product_{k=1..n} (1 - x*Q^(3*k))/(1 + x*Q^(3*k)) due to a q-series expansion for the Jacobi theta_4 function. LINKS Table of n, a(n) for n=0..18. EXAMPLE G.f.: A(x) = 1 + 2*x + 14*x^2 + 158*x^3 + 2274*x^4 + 37410*x^5 +... where A(x) = 1 + 2*x*A(x)^3 + 2*x^2*A(x)^12 + 2*x^3*A(x)^27 + 2*x^4*A(x)^48 + ... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, 2*x^m*(A+x*O(x^n))^(3*m^2))); polcoeff(A, n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A176719, A218294. Sequence in context: A332693 A196791 A349312 * A354242 A268011 A052112 Adjacent sequences: A218292 A218293 A218294 * A218296 A218297 A218298 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 26 2012 STATUS approved

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Last modified September 28 18:05 EDT 2023. Contains 365736 sequences. (Running on oeis4.)