A144658 - OEIS

%I #14 Aug 14 2019 14:15:49

%S 0,6,222,5052,109512,2432448,55611294,1301187912,30992726652,

%T 748573575780,18283412752602,450657126652626,11192820097106112,

%U 279787295335659972,7032532241701837758,177611430241032329568

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

%H Seiichi Manyama, <a href="/A144658/b144658.txt">Table of n, a(n) for n = 0..100</a>

%t Table[Sum[Sum[Sum[(i+j+k)!/i!/j!/k!,{i,1,n}],{j,1,n}],{k,1,n}],{n,1,30}]

%o (PARI) {a(n) = sum(i=1, n, sum(j=1, n, sum(k=1, n, (i+j+k)!/(i!*j!*k!))))} \\ _Seiichi Manyama_, May 19 2019

%o (PARI) {a(n) = sum(i=3, 3*n, i!*polcoef(sum(j=1, n, x^j/j!)^3, i))} \\ _Seiichi Manyama_, May 19 2019

%Y Cf. A144511.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jan 30 2009