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

0,3

Links

Table of n, a(n) for n=0..20.

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.

Example

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.

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 *)

Prog

(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 */

Crossrefs

Sequence in context: A302581 A305460 A073767 * A208975 A286794 A176043

Adjacent sequences: A226346 A226347 A226348 * A226350 A226351 A226352

Keyword

nonn

Author

Geoffrey Critzer, Jun 04 2013

Status

approved