A318392 Regular triangle where T(n,k) is the number of pairs of set partitions of {1,...,n} with join of length k.

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

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