OFFSET
1,2
FORMULA
E.g.f.: (Sum_{n>=0} B(n)^2 x^n/n!)^t where B = A000110.
EXAMPLE
The T(3,2) = 9 pairs of set partitions:
{{1},{2},{3}} {{1},{2,3}}
{{1},{2},{3}} {{1,2},{3}}
{{1},{2},{3}} {{1,3},{2}}
{{1},{2,3}} {{1},{2},{3}}
{{1},{2,3}} {{1},{2,3}}
{{1,2},{3}} {{1},{2},{3}}
{{1,2},{3}} {{1,2},{3}}
{{1,3},{2}} {{1},{2},{3}}
{{1,3},{2}} {{1,3},{2}}
Triangle begins:
1
3 1
15 9 1
119 87 18 1
1343 1045 285 30 1
19905 15663 4890 705 45 1
MATHEMATICA
nn=5; Table[n!*SeriesCoefficient[Sum[BellB[n]^2*x^n/n!, {n, 0, nn}]^t, {x, 0, n}, {t, 0, k}], {n, nn}, {k, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Aug 25 2018
STATUS
approved