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A144661
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a(n) = Sum_{i=0..n} Sum_{j=0..n} Sum_{k=0..n} Sum_{l=0..n} (i+j+k+l)!/(i!*j!*k!*l!).
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5
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1, 65, 7365, 1107697, 191448941, 35899051101, 7101534312685, 1458965717496881, 308290573348183629, 66577182435768923245, 14629025943480502591445, 3260160391173522631759533, 735119604833362632050789701, 167408468505328518543519208949, 38448088693846486556578015883325
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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^(8*n + 15/2) / (81 * Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Apr 02 2019
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MAPLE
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f:=n->add( add( add( add( (i+j+k+l)!/(i!*j!*k!*l!), i=0..n), j=0..n), k=0..n), l=0..n); [seq(f(n), n=0..20)];
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MATHEMATICA
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Table[Sum[(i + j + k + l)! / (i!*j!*k!*l!), {i, 0, n}, {j, 0, n}, {k, 0, n}, {l, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 02 2019 *)
Table[Sum[(1 + j + k + l + n)!/((1 + j + k + l)*j!*k!*l!), {j, 0, n}, {k, 0, n}, {l, 0, n}] / n!, {n, 0, 20}] (* Vaclav Kotesovec, Apr 03 2019 *)
Table[Sum[(1 + k + l + 2*n)! * HypergeometricPFQ[{1, -1 - k - l - n, -n}, {-1 - k - l - 2*n, -k - l - n}, 1] / ((1 + k + l + n)*k!*l!*n!), {k, 0, n}, {l, 0, n}]/n!, {n, 0, 20}] (* Vaclav Kotesovec, Apr 03 2019 *)
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PROG
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(PARI) {a(n) = sum(i=0, n, sum(j=0, n, sum(k=0, n, sum(l=0, n, (i+j+k+l)!/(i!*j!*k!*l!)))))} \\ Seiichi Manyama, Apr 02 2019
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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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