A035052 Number of sets of rooted connected graphs where every block is a complete graph.

1, 1, 2, 5, 14, 42, 134, 444, 1518, 5318, 18989, 68856, 252901, 938847, 3517082, 13278844, 50475876, 193014868, 741963015, 2865552848, 11113696421, 43266626430, 169019868095, 662337418989, 2602923589451, 10256100717875

Offset

0,3

Links

T. D. Noe, Table of n, a(n) for n=0..200

Loic Foissy, The Hopf algebra of Fliess operators and its dual pre-Lie algebra, 2013.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 862

N. J. A. Sloane, Transforms

Formula

Euler transform of A007563.

a(n) ~ c * d^n / n^(3/2), where d = 4.189610958393826965527036454524... (see A245566), c = 0.35683683547585... . - Vaclav Kotesovec, Jul 26 2014

Maple

with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; `if`(n=0, 1, add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n) end end: b:= etr(aa): c:= etr(b): aa:= n-> if n=0 then 0 else c(n-1) fi: a:= etr(aa): seq(a(n), n=0..25); # Alois P. Heinz, Sep 09 2008

Mathematica

etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[ j]}]*b[n-j], {j, 1, n}]/n]; b]; b = etr[aa]; c = etr[b]; aa = Function[{n}, If[n == 0, 0, c[n-1]]]; a = etr[aa]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Mar 05 2015, after Alois P. Heinz *)

Prog

(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(v=[1]); for(i=2, n, v=concat([1], EulerT(EulerT(v)))); concat([1], EulerT(v))} \\ Andrew Howroyd, May 20 2018

Crossrefs

Cf. A007549, A007563, A030019, A035051, A035053.

Cf. A245566.

Sequence in context: A202061 A346660 A129086 * A148330 A149876 A165146

Adjacent sequences: A035049 A035050 A035051 * A035053 A035054 A035055

Keyword

nonn

Author

Christian G. Bower, Oct 15 1998

Status

approved