A226349 Number of functions f:{1,2,...,n} -> {1,2,...,n} such that the 1 and the 2 are in the same component of the functional digraph representation of f.

0, 0, 3, 20, 188, 2280, 33864, 595196, 12081600, 278122032, 7159299200, 203771364324, 6354217539072, 215429796291320, 7889813961243648, 310413633428119500, 13057068314325008384, 584737112800511959104, 27776659696045110558720, 1395009275793285886030772, 73854320834079368232960000

Offset: 0

Author

Geoffrey Critzer, Jun 04 2013

Keywords

• nonn

Examples

			a(3)=20 because there are 17 connected functions on [3] and (2,1,3), (1,1,3), (2,2,3) where the functions are represented by their values.
		

Programs

Mathematica

nn=18; t=Sum[n^(n-1)x^n/n!, {n,1,nn+2}]; Join[{0,0}, Range[0,nn]! CoefficientList[Series[D[D[Log[1/(1-t)], x], x]/(1-t), {x,0,nn}], x]]
a[ n_] := If[ n < 2, 0, With[ {m = n - 2}, With[ {t = 1 + Sum[k^k x^k/k!, {k, m + 2}]}, m! SeriesCoefficient[ D[ Log[ t], {x, 2}] t, {x, 0, m} ]]]] (* Michael Somos, Jun 04 2013 *)

PARI

{a(n) = local(A); if( n<2, 0, m = n-2; A = sum( k=0, m+2, k^k * x^k / k!, x^3 * O(x^m)); m! * polcoeff( log(A)'' * A, m))} /* Michael Somos, Jun 04 2013 */

Formula

E.g.f. is the double integral of A''(x)*B(x) dx^2 where A(x) is the e.g.f. for A001865 and B(x) is the e.g.f. for A000312.