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 A213409 G.f.: exp( Sum_{n>=1} binomial(3*n^2,n^2) * x^n/n ). 4
 1, 3, 252, 1563022, 563716946982, 10517711119760250261, 9692061982207456039533424586, 430311348543725825536505706371595438684, 906895928239445077568583988067142630846220290783969, 89857639488565787203362892584824012528872539028234934088960440084 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Compare to the g.f. G(x) = 1 + x*G(x)^3 of A001764: G(x)^3 = exp( Sum_{n>=1} binomial(3*n,n) * x^n/n ). LINKS G. C. Greubel, Table of n, a(n) for n = 0..34 FORMULA a(n) = (1/n) * Sum_{k=1..n} binomial(3*k^2,k^2) * a(n-k) for n>0 with a(0)=1. a(n) ~ sqrt(3) * (27/4)^(n^2) / (2*sqrt(Pi)*n^2). - Vaclav Kotesovec, Mar 06 2014 EXAMPLE G.f.: A(x) = 1 + 3*x + 252*x^2 + 1563022*x^3 + 563716946982*x^4 +... where log(A(x)) = 3*x + 495*x^2/2 + 4686825*x^3/3 + 2254848913647*x^4/4 + 52588547141148893628*x^5/5 +...+ C(3*n^2,n^2)*x^n/n +... MATHEMATICA nmax = 10; b = ConstantArray[0, nmax+1]; b[[1]] = 1; Do[b[[n+1]] = 1/n*Sum[Binomial[3*k^2, k^2]*b[[n-k+1]], {k, 1, n}], {n, 1, nmax}]; b (* Vaclav Kotesovec, Mar 06 2014 *) PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n, binomial(3*m^2, m^2)*x^m/m)+x*O(x^n)), n)} (PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, binomial(3*k^2, k^2)*a(n-k)))} CROSSREFS Cf. A201556, A213410, A001764, A245245 (log). Sequence in context: A025418 A075901 A028918 * A227028 A279653 A320023 Adjacent sequences: A213406 A213407 A213408 * A213410 A213411 A213412 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 10 2012 STATUS approved

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Last modified August 15 10:04 EDT 2024. Contains 375173 sequences. (Running on oeis4.)