A144511 a(n) = Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} (i+j+k)!/(3!*i!*j!*k!).

0, 1, 37, 842, 18252, 405408, 9268549, 216864652, 5165454442, 124762262630, 3047235458767, 75109521108771, 1865470016184352, 46631215889276662, 1172088706950306293, 29601905040172054928, 750748513858793527974, 19110455782881086439234, 488057675380082251617235

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..100

Moa Apagodu, David Applegate, N. J. A. Sloane, and Doron Zeilberger, Analysis of the Gift Exchange Problem, arXiv:1701.08394, 2017.

David Applegate and N. J. A. Sloane, The Gift Exchange Problem (arXiv:0907.0513, 2009)

Formula

a(n) = (5 + 3*n - 3*binomial(2*n+2, n+1) + A144660(n))/6. - Vaclav Kotesovec, Apr 04 2019

Maple

f:=n->add( add( add( (i+j+k)!/(3!*i!*j!*k!), i=1..n), j=1..n), k=1..n); [seq(f(n), n=0..20)];

Mathematica

Table[Sum[Sum[Sum[(i+j+k)!/i!/j!/k!/6, {i, 1, n}], {j, 1, n}], {k, 1, n}], {n, 1, 30}]
Table[(5 + 3*n - 3*Binomial[2*n+2, n+1] + Sum[(1 + k + 2*n)! * HypergeometricPFQ[{1, -1 - k - n, -n}, {-1 - k - 2*n, -k - n}, 1] / ((1 + k + n)*k!*n!^2), {k, 0, n}]) / 6, {n, 0, 20}] (* Vaclav Kotesovec, Apr 04 2019 *)

Prog

(PARI) {a(n) = sum(i=1, n, sum(j=1, n, sum(k=1, n, (i+j+k)!/(6*i!*j!*k!))))} \\ Seiichi Manyama, Apr 03 2019
(PARI) {a(n) = sum(i=3, 3*n, i!*polcoef(sum(j=1, n, x^j/j!)^3, i))/6} \\ Seiichi Manyama, May 19 2019

Crossrefs

Column 3 of array in A144510.

Cf. A144658, A144660 (a very similar sum).

Sequence in context: A216439 A333065 A251105 * A028225 A028223 A028217

Adjacent sequences: A144508 A144509 A144510 * A144512 A144513 A144514

Keyword

nonn

Author

David Applegate and N. J. A. Sloane, Dec 15 2008, Jan 30 2009

Status

approved