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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.
1
0, 0, 3, 20, 188, 2280, 33864, 595196, 12081600, 278122032, 7159299200, 203771364324, 6354217539072, 215429796291320, 7889813961243648, 310413633428119500, 13057068314325008384, 584737112800511959104, 27776659696045110558720, 1395009275793285886030772, 73854320834079368232960000
OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jun 04 2013
STATUS
approved