A198046 Exponential transform of A053549.

1, 1, 3, 19, 225, 4841, 192355, 14537643, 2135997537, 616565334097, 351243585487331, 395958973398105283, 885030941975862363649, 3928075680727698371316537, 34658158001445631936261356547, 608435501761943981290097259909211

Offset

0,3

Comments

a(n) is the number of ways to designate a node in each connected component over all simple labeled graphs on n nodes.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..80

Formula

E.g.f.: exp(A(x)) where A(x) is the e.g.f. for A053549.

Maple

g:= proc(n) option remember; `if`(n=0, 1, 2^(n*(n-1)/2)-
      add(k*binomial(n, k)* 2^((n-k)*(n-k-1)/2)*g(k), k=1..n-1)/n)
    end:
a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n-1, j-1) *j*g(j) *a(n-j), j=1..n))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Mar 17 2015

Mathematica

nn=20; a=Sum[2^Binomial[n, 2]x^n/n!, {n, 0, nn}]; Range[0, nn]! CoefficientList[Series[Exp[x D[Log[a], x]], {x, 0, nn}], x]

Prog

(PARI) seq(n)={Vec(serlaplace(exp(x*deriv(log(sum(k=0, n, 2^binomial(k, 2) * x^k / k!) + O(x*x^n))))))} \\ Andrew Howroyd, Jun 18 2018

Crossrefs

Cf. A053549.

Sequence in context: A003111 A160888 A126444 * A295812 A228229 A323875

Adjacent sequences: A198043 A198044 A198045 * A198047 A198048 A198049

Keyword

nonn

Author

Geoffrey Critzer, Oct 20 2011

Extensions

a(6), a(10) corrected by Alois P. Heinz, Mar 18 2015

Status

approved