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 A112035 a(n) = Sum_{k=0..n} k*C(n,k)^2*C(n+k,k)^3, where C := binomial. 2
 0, 8, 540, 42576, 3675000, 334595040, 31539372732, 3046472028320, 299666635774704, 29894793786770040, 3016010007220052700, 307083034957464057600, 31506217163866419507000, 3253427167078021753747200, 337821983730064508845772700, 35246436592815103238009282880 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..15. C. Elsner, On recurrence formulas for sums involving binomial coefficients, Fibonacci Quarterly, 43,1 (2005), 31-45. MATHEMATICA Table[Sum[k*Binomial[n, k]^2*Binomial[n + k, k]^3, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 10 2021 *) PROG (PARI) a(n) = sum(k=0, n, k*binomial(n, k)^2*binomial(n+k, k)^3); \\ Michel Marcus, Mar 10 2016 CROSSREFS Cf. A055246 (indices where not multiple of 3), A112036. Sequence in context: A216353 A145182 A089671 * A200706 A266207 A027536 Adjacent sequences: A112032 A112033 A112034 * A112036 A112037 A112038 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 28 2005 STATUS approved

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Last modified May 22 18:14 EDT 2024. Contains 372758 sequences. (Running on oeis4.)