A248844 - OEIS

%I #28 Aug 07 2015 10:57:01

%S 1,1,2,4,6,6,3,9,24,54,90,90,4,16,60,204,600,1440,2520,2520,5,25,120,

%T 540,2220,8100,25200,63000,113400,113400,6,36,210,1170,6120,29520,

%U 128520,491400,1587600,4082400,7484400,7484400,7,49,336,2226,14070,83790,463680,2346120,10636920,42071400,139708800,366735600,681080400,681080400

%N Triangle read by rows: T(m,n) = number of ways of distributing n distinguishable balls into m distinguishable bins of size 2 where empty bins are permitted (m >= 1, 1 <= n <= 2m).

%H Marko R. Riedel, <a href="http://math.stackexchange.com/questions/975503">Distinguishable balls into distinguishable boxes with a maximum capacity</a>

%F E.g.f. for row m: (sum(k=0..s) z^k/k!)^m, s=2.

%e Triangle T(n, m) is:

%e 1, 1;

%e 2, 4, 6, 6;

%e 3, 9, 24, 54, 90, 90;

%e 4, 16, 60, 204, 600, 1440, 2520, 2520;

%e 5, 25, 120, 540, 2220, 8100, 25200, 63000, 113400, 113400;

%p P := proc(n, m, s) n!*coeftayl(add(z^k/k!, k=0..s)^m, z=0, n); end;

%t Table[nn = 2 n;Drop[Range[0, nn]! CoefficientList[Series[(1 + x + x^2/2!)^n, {x, 0, nn}], x], 1], {n,0,7}] // Flatten (* _Geoffrey Critzer_, Aug 07 2015 *)

%K nonn,tabf

%O 1,3

%A _Marko Riedel_, Oct 15 2014