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A220690 Number of acyclic graphs on {1,2,...,n} such that the node with label 1 is in the same connected component (tree) as the node with label 2. 2
0, 0, 1, 4, 24, 198, 2110, 27768, 436656, 8003950, 167779068, 3961727820, 104102329504, 3013887239454, 95338047836520, 3272043459321328, 121106541865151040, 4808924948167249302, 203931444227955436816, 9198925314402386788500, 439809753701222702598528 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
E.g.f.: Double integral of U''(x)*exp(U(x)) dx^2 where U(x) is the e.g.f. for A000272.
a(n) = Sum_{k=0..n-2} binomial(n-2,k)*(k+2)^k*A001858(n-k-2).
MAPLE
b:= proc(n) option remember; `if`(n=0, 1,
add(binomial(n-1, j) *(j+1)^(j-1) *b(n-1-j), j=0..n-1))
end:
a:= n-> add(binomial(n-2, k)*(k+2)^k*b(n-k-2), k=0..n-2):
seq(a(n), n=0..20); # Alois P. Heinz, Apr 13 2013
MATHEMATICA
nn=20; u=Sum[n^(n-2)x^n/n!, {n, 1, nn}]; Range[0, nn]!CoefficientList[ Series[Integrate[Integrate[D[D[u, x], x]Exp[u], x], x], {x, 0, nn}], x]
PROG
(PARI)
N = 66; x = 'x + O('x^N);
U = sum(n=1, N, n^(n-2)*x^n/n!);
egf = intformal(intformal( deriv(deriv(U)) * exp(U) ));
gf = serlaplace(egf) + 'c0;
v = Vec(gf); v[1]-='c0; v
/* Joerg Arndt, Apr 13 2013 */
CROSSREFS
Cf. A221864.
Sequence in context: A201338 A362355 A099021 * A136229 A138419 A366341
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Apr 13 2013
STATUS
approved

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Last modified April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)