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A035052 Number of sets of rooted connected graphs where every block is a complete graph. 5
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A061815 A202061 A129086 * A148330 A149876 A165146

Adjacent sequences:  A035049 A035050 A035051 * A035053 A035054 A035055

KEYWORD

nonn

AUTHOR

Christian G. Bower, Oct 15 1998

STATUS

approved

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Last modified January 18 01:36 EST 2019. Contains 319260 sequences. (Running on oeis4.)