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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

Table of n, a(n) for n=0..18.

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: A234463 A194044 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 February 18 05:48 EST 2018. Contains 299298 sequences. (Running on oeis4.)