A306432
a(n) = Sum_{0<=i
Original entry on oeis.org
0, 0, 3, 77, 1777, 41088, 964199, 22962721, 553886872, 13504654074, 332253097450, 8237141855085, 205552200503455, 5158397884289338, 130087682458168777, 3294763277704155587, 83764781257030939439, 2136808562574516060202, 54674217200832983666877
Offset: 0
-
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
-
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 *)
-
{a(n) = sum(i=0, n, sum(j=i+1, n, sum(k=j+1, n, (i+j+k)!/(i!*j!*k!))))}
A307353
a(n) = Sum_{1<=i<=j<=k<=n} (i+j+k)!/(i!*j!*k!).
Original entry on oeis.org
0, 6, 138, 2808, 59083, 1298797, 29538183, 688783509, 16365391557, 394523905488, 9621386549905, 236859066714283, 5876752842394018, 146774130963028054, 3686474939155802036, 93044751867415156290, 2358431594463240429469
Offset: 0
-
Table[Sum[Sum[Sum[(i+j+k)!/(i!*j!*k!), {i, 1, j}], {j, 1, k}], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 04 2019 *)
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{a(n) = sum(i=1, n, sum(j=i, n, sum(k=j, n, (i+j+k)!/(i!*j!*k!))))}
A307358
a(n) = Sum_{0<=i<=j<=k<=n} (-1)^(i+j+k) * (i+j+k)!/(i!*j!*k!).
Original entry on oeis.org
1, -4, 72, -1345, 27886, -610558, 13861334, -322838475, 7663363513, -184598740512, 4498935186891, -110693299767349, 2745124008220296, -68532209858173364, 1720678086867077832, -43415209670536390089, 1100146390869600888470
Offset: 0
-
Table[Sum[Sum[Sum[(-1)^(i+j+k) * (i+j+k)!/(i!*j!*k!), {i, 0, j}], {j, 0, k}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 04 2019 *)
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{a(n) = sum(i=0, n, sum(j=i, n, sum(k=j, n, (-1)^(i+j+k)*(i+j+k)!/(i!*j!*k!))))}
Showing 1-3 of 3 results.