A226358 - OEIS

%I #8 Jun 05 2013 21:02:51

%S 0,0,12,456,63264,33261504,68578235904,562670659193856,

%T 18444482155274686464,2417777758564741377613824,

%U 1267640925339738611935051382784,2658450920454274160572632643718086656,22300734564407398196216147429929635837640704

%N Number of labeled relations on {1,2,...,n} such that 1 and 2 are in the same component.

%C A062738(n) < a(n) < A002416 for n > 2.

%F E.g.f. is the double integral of A''(x)*B(x) where A(x) is the e.g.f. for A062738 and B(x) is the e.g.f. for A002416.

%e a(3) = 456 because there are 432 connected relations on [3].  Then there are 12 connected relations on [2] and for each the element 3 may be related to itself or not.

%e 432 + 2*12 = 456.

%t nn=10; g=Sum[2^n^2 x^n/n!, {n, 0, nn+2}]; Join[{0,0}, Range[0,nn]! * CoefficientList[Series[D[D[Log[g],x],x]g ,{x, 0, nn}], x]]

%Y Cf. A226349, A224510.

%K nonn

%O 0,3

%A _Geoffrey Critzer_, Jun 04 2013