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 A213410 G.f.: exp( Sum_{n>=1} binomial(3*n,n)^n/3^n * x^n/n ). 1
 1, 1, 13, 7330, 185307558, 201002187396362, 9357300769149011773697, 18775362849239140086719414696830, 1631039199744298058694966065590003308698494, 6159916689356522044764167426829149420348399496664634288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare to the g.f. G(x) = 1 + x*G(x)^3 of A001764: G(x) = exp( Sum_{n>=1} binomial(3*n,n)/3 * x^n/n ). LINKS Table of n, a(n) for n=0..9. FORMULA a(n) = (1/n) * Sum_{k=1..n} binomial(3*k,k)^k/3^k * a(n-k) for n>0 with a(0)=1. EXAMPLE G.f.: A(x) = 1 + x + 13*x^2 + 7330*x^3 + 185307558*x^4 + 201002187396362*x^5 +... where log(A(x)) = x + 5^2*x^2/2 + 28^3*x^3/3 + 165^4*x^4/4 + 1001^5*x^5/5 + 6188^6*x^6/6 + 38760^7*x^7/7 +...+ A025174(n)^n*x^n/n +... MATHEMATICA nmax = 10; b = ConstantArray[0, nmax+1]; b[[1]] = 1; Do[b[[n+1]] = 1/n*Sum[Binomial[3*k, k]^k/3^k * 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, m)^m/3^m*x^m/m)+x*O(x^n)), n)} for(n=0, 15, print1(a(n), ", ")) CROSSREFS Cf A213409, A001764, A025174, A200002. Sequence in context: A203585 A191937 A210157 * A013524 A060887 A020521 Adjacent sequences: A213407 A213408 A213409 * A213411 A213412 A213413 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 10 2012 STATUS approved

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Last modified August 10 15:59 EDT 2024. Contains 375057 sequences. (Running on oeis4.)