A144662 a(n) = Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} Sum_{l=1..n} (i+j+k+l)!/(4!*i!*j!*k!*l!).

0, 1, 266, 45296, 7958726, 1495388159, 295887993624, 60790021361170, 12845435390707724, 2774049143394729653, 609542744597785306189, 135840016223787254538508, 30629983532857972983331740, 6975352854342057056747327899, 1602003695575764851150428242804, 370631496919828403109950449644134

Offset: 0

Author

N. J. A. Sloane, Feb 01 2009

Keywords

• nonn

Links

• 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)

Crossrefs

Column 4 of A144512. Cf. A144660, A144661.

Programs

Maple

f:=n->add( add( add( add( (i+j+k+l)!/(4!*i!*j!*k!*l!), i=1..n),j=1..n),k=1..n),l=1..n); [seq(f(n),n=0..16)];

Mathematica

a[n_] := Sum[(i+j+k+l)!/(4! i! j! k! l!), {i, n}, {j, n}, {k, n}, {l, n}];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Sep 05 2018 *)
Table[(Binomial[2*n + 2, n + 1] - 2*(1 + n) + 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!)^2) - (2*(1 + k + l + n)!)/((1 + k + l) k! l! n!), {k, 1, n}, {l, 1, n}])/24, {n, 0, 15}] (* Vaclav Kotesovec, Apr 04 2019 *)