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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..45.

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.

Cf. A000110, A000258, A008277, A048994, A059849, A181939, A318389, A318390, A318391, A318393.

Sequence in context: A134144 A035342 A039815 * A329059 A147453 A147020

Adjacent sequences:  A318389 A318390 A318391 * A318393 A318394 A318395

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Aug 25 2018

STATUS

approved

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Last modified June 4 07:23 EDT 2020. Contains 334822 sequences. (Running on oeis4.)