A167128 - OEIS

%I #12 Jun 05 2016 23:48:10

%S 1,1,2,1,12,5,1,56,84,15,1,240,1025,510,52,1,992,10980,12155,3030,203,

%T 1,4032,109865,250250,119700,18396,877,1,16256,1056804,4754295,

%U 4037250,1093526,115892,4140,1,65280,9925025,85866270,125131902,54634608

%N Triangle T(m,n) read by rows: T(m,n) = Sum_{k=1..n} StirlingS2(m, n) * StirlingS2(m, k).

%C Row sums are: {1, 3, 18, 156, 1828, 27361, 503121, 11078164, 286158309, 8532624076,...}

%H G. C. Greubel, <a href="/A167128/b167128.txt">Table of n, a(n) for the first 50 rows</a>

%e {1},

%e {1, 2},

%e {1, 12, 5},

%e {1, 56, 84, 15},

%e {1, 240, 1025, 510, 52},

%e {1, 992, 10980, 12155, 3030, 203},

%e {1, 4032, 109865, 250250, 119700, 18396, 877},

%e {1, 16256, 1056804, 4754295, 4037250, 1093526, 115892, 4140},

%e {1, 65280, 9925025, 85866270, 125131902, 54634608, 9752820, 761256, 21147},

%e {1, 261632, 91825860, 1498812435, 3677221800, 2494968273, 677252520, 86946750, 5218830, 115975}

%t T[m_, n_] = Sum[StirlingS2[m, n]*StirlingS2[m, k], {k, 1, n}];

%t Flatten[Table[Table[T[m, n], {n, 1, m}], {m, 1, 10}]]

%K nonn,tabl

%O 1,3

%A _Roger L. Bagula_, Oct 28 2009

%E  Edited by the OEIS editors, Jun 05 2016