cp's OEIS Frontend

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

%I A318392 #5 Sep 15 2018 15:43:52
%S A318392 1,3,1,15,9,1,119,87,18,1,1343,1045,285,30,1,19905,15663,4890,705,45,
%T A318392 1,369113,286419,95613,16450,1470,63,1,8285261,6248679,2147922,410053,
%U A318392 44870,2730,84,1,219627683,159648795,55211229,11202534,1394883,105714,4662,108,1
%N A318392 Regular triangle where T(n,k) is the number of pairs of set partitions of {1,...,n} with join of length k.
%F A318392 E.g.f.: (Sum_{n>=0} B(n)^2 x^n/n!)^t where B = A000110.
%e A318392 The T(3,2) = 9 pairs of set partitions:
%e A318392   {{1},{2},{3}}  {{1},{2,3}}
%e A318392   {{1},{2},{3}}  {{1,2},{3}}
%e A318392   {{1},{2},{3}}  {{1,3},{2}}
%e A318392    {{1},{2,3}}  {{1},{2},{3}}
%e A318392    {{1},{2,3}}   {{1},{2,3}}
%e A318392    {{1,2},{3}}  {{1},{2},{3}}
%e A318392    {{1,2},{3}}   {{1,2},{3}}
%e A318392    {{1,3},{2}}  {{1},{2},{3}}
%e A318392    {{1,3},{2}}   {{1,3},{2}}
%e A318392 Triangle begins:
%e A318392       1
%e A318392       3     1
%e A318392      15     9     1
%e A318392     119    87    18     1
%e A318392    1343  1045   285    30     1
%e A318392   19905 15663  4890   705    45     1
%t A318392 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}]
%Y A318392 Row sums are A001247. First column is A060639.
%Y A318392 Cf. A000110, A000258, A008277, A048994, A059849, A181939, A318389, A318390, A318391, A318393.
%K A318392 nonn,tabl
%O A318392 1,2
%A A318392 _Gus Wiseman_, Aug 25 2018