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A089671
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a(n) = S3(n,3), where S3(n, t) = Sum_{k=0..n} k^t *(Sum_{j=0..k} binomial(n,j))^3.
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4
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0, 8, 539, 16632, 364042, 6510160, 101817234, 1447146512, 19144522160, 239513659776, 2865559784050, 33052451375152, 369790434398988, 4031805422883680, 42996629236138928, 449821323139340160, 4627609615665499456, 46907404618252667392, 469254490696475078130
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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) = Sum_{k=0..n} k^3 *(Sum_{j=0..k} binomial(n,j))^3. - G. C. Greubel, May 26 2022
a(n) ~ 15 * 2^(3*n-6) * n^4 * (1 - 2/(5*sqrt(Pi*n)) + (2 - sqrt(3)/(5*Pi))/n). - Vaclav Kotesovec, May 27 2022
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MATHEMATICA
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a[n_]:= a[n]= Sum[k^3*(Sum[Binomial[n, j], {j, 0, k}])^3, {k, 0, n}];
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PROG
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(SageMath)
def A089671(n): return sum(k^3*(sum(binomial(n, j) for j in (0..k)))^3 for k in (0..n))
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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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