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A219564
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Sum(binomial(n+k,k)^6, k=0..n).
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7
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1, 65, 47386, 65004097, 119498671876, 260128695981674, 632156164654144530, 1659900189891175027265, 4616088190888638302435080, 13418259230056806455830305940, 40401802613222456104862752944356, 125182282922559710456869140648653290, 397195659937314116991934285462527257236
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) ~ 2^(12*n+6)/(63*Pi^3*n^3)
Generally (for q > 0), Sum_{k=0..n} C(n + k,k)^q is asymptotic to 2^((2*n+1)*q)/((2^q-1)*(Pi*n)^(q/2)) * (1 - q/(2*n)*(1/4+1/(2^q-1)^2) + O(1/n^2))
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MATHEMATICA
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Table[Sum[Binomial[n+k, k]^6, {k, 0, n}], {n, 0, 20}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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