A119582 - OEIS

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A119582

a(n) = (n^2+n^3)*(binomial(2*n,n))/2.

0, 2, 36, 360, 2800, 18900, 116424, 672672, 3706560, 19691100, 101615800, 512143632, 2531090016, 12303909800, 58971402000, 279211536000, 1307950928640, 6069709778220, 27933266453400, 127596402318000, 578955421044000, 2611088948908440, 11711414832065520, 52265818258804800

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..23.

FORMULA

From Amiram Eldar, Sep 04 2022: (Start)

a(n) = A011379(n)*A000984(n)/2.

Sum_{n>=1} 1/a(n) = 2*Pi/sqrt(3) - Pi^2/9 - 2.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2 - 4*sqrt(5)*log(phi) + 12*log(phi)^2, where phi is the golden ratio (A001622). (End)

MAPLE

[seq ((n^2+n^3)*(binomial(2*n, n))/2, n=0..29)];