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 A199813 G.f.: exp( Sum_{n>=1} A000984(n)*A000172(n) * x^n/n ), which involves central binomial coefficients (A000984) and Franel numbers (A000172). 2
 1, 4, 38, 504, 8249, 154036, 3149326, 68741880, 1576163328, 37548785408, 922252542128, 23222906277952, 596981991939677, 15616173859832740, 414621835401615110, 11150969618415168280, 303278916800906999191, 8330190277527648516572, 230814933905555392525290 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sum_{k=0..n} C(n,k)^2 = A000984(n) defines central binomial coefficients. Sum_{k=0..n} C(n,k)^3 = A000172(n) defines Franel numbers. LINKS EXAMPLE G.f.: A(x) = 1 + 4*x + 38*x^2 + 504*x^3 + 8249*x^4 + 154036*x^5 +... where log(A(x)) = 2*2*x + 6*10*x^2/2 + 20*56*x^3/3 + 70*346*x^4/4 + 252*2252*x^5/5 + 924*15184*x^6/6 +...+ A000984(n)*A000172(n)*x^n/n +... PROG (PARI) {a(n)=polcoeff(exp(sum(m=1, n, binomial(2*m, m)*sum(k=0, m, binomial(m, k)^3)*x^m/m)+x*O(x^n)), n)} CROSSREFS Cf. A199816, A181418, A000984, A000172. Sequence in context: A194044 A317605 A263376 * A120974 A113664 A217900 Adjacent sequences:  A199810 A199811 A199812 * A199814 A199815 A199816 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 10 2011 STATUS approved

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Last modified January 18 10:53 EST 2019. Contains 319271 sequences. (Running on oeis4.)