A226358 Number of labeled relations on {1,2,...,n} such that 1 and 2 are in the same component.

0, 0, 12, 456, 63264, 33261504, 68578235904, 562670659193856, 18444482155274686464, 2417777758564741377613824, 1267640925339738611935051382784, 2658450920454274160572632643718086656, 22300734564407398196216147429929635837640704

Offset: 0

Author

Geoffrey Critzer, Jun 04 2013

Keywords

• nonn

Comments

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

Examples

			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.
432 + 2*12 = 456.
		

Crossrefs

Cf. A226349, A224510.

Programs

Mathematica

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]]

Formula

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.