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A318392
Regular triangle where T(n,k) is the number of pairs of set partitions of {1,...,n} with join of length k.
9
1, 3, 1, 15, 9, 1, 119, 87, 18, 1, 1343, 1045, 285, 30, 1, 19905, 15663, 4890, 705, 45, 1, 369113, 286419, 95613, 16450, 1470, 63, 1, 8285261, 6248679, 2147922, 410053, 44870, 2730, 84, 1, 219627683, 159648795, 55211229, 11202534, 1394883, 105714, 4662, 108, 1
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
Row sums are A001247. First column is A060639.
Sequence in context: A134144 A035342 A039815 * A329059 A147453 A147020
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Aug 25 2018
STATUS
approved