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A089670
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a(n) = S3(n,2), 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, 283, 6044, 101360, 1470640, 19361174, 237684384, 2768042208, 30935313600, 334481353690, 3519672963752, 36206551801264, 365363625058432, 3626585989411280, 35485636769545600, 342894590805622656, 3276865150482420480, 31008279252965786178
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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^2 *(Sum_{j=0..k} binomial(n,j))^3. - G. C. Greubel, May 26 2022
a(n) ~ 7/24 * 8^n * n^3 * (1 - 9/(14*sqrt(Pi*n)) + (12/7 - 3^(3/2)/(14*Pi))/n). - Vaclav Kotesovec, May 27 2022
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MATHEMATICA
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a[n_]:= a[n]= Sum[k^2*(Sum[Binomial[n, j], {j, 0, k}])^3, {k, 0, n}];
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PROG
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(SageMath)
def A089670(n): return sum(k^2*(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,easy
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AUTHOR
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STATUS
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approved
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