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A306432
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a(n) = Sum_{0<=i<j<k<=n} (i+j+k)!/(i!*j!*k!).
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2
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0, 0, 3, 77, 1777, 41088, 964199, 22962721, 553886872, 13504654074, 332253097450, 8237141855085, 205552200503455, 5158397884289338, 130087682458168777, 3294763277704155587, 83764781257030939439, 2136808562574516060202, 54674217200832983666877
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OFFSET
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0,3
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LINKS
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FORMULA
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MAPLE
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g:= proc(n) local i, j;
add(add((i+j+n)!/(i!*j!*n!), j=i+1..n-1), i=0..n-2)
end proc:
ListTools:-PartialSums(map(g, [$0..30])); # Robert Israel, May 16 2019
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MATHEMATICA
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Table[Sum[Sum[Sum[(i + j + k)!/(i!*j!*k!), {i, 0, j-1}], {j, 0, k-1}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 05 2019 *)
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PROG
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(PARI) {a(n) = sum(i=0, n, sum(j=i+1, n, sum(k=j+1, n, (i+j+k)!/(i!*j!*k!))))}
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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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