OFFSET
0,4
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 71, (3.4.13).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1600 (first 200 terms from T. D. Noe)
Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465 [math.CO], 2016.
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, arXiv:math/0205301 [math.CO], 2002; Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 167
N. J. A. Sloane, Transforms
FORMULA
Shifts left when Euler transform is applied twice.
a(n) ~ c * d^n / n^(3/2), where d = 4.189610958393826965527036454524044275... (see A245566), c = 0.1977574301782950818433893126632477845870281049591883888... . - Vaclav Kotesovec, Jul 26 2014
MAPLE
with(numtheory): etr:= proc(p) local b; b:= proc(n) option remember; if n=0 then 1 else (add(d*p(d), d=divisors(n)) +add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n-1))/n fi end end: b:= etr(a): c:= etr(b): a:= n-> if n=0 then 0 else c(n-1) fi: seq(a(n), n=0..25); # Alois P. Heinz, Sep 06 2008
MATHEMATICA
etr[p_] := 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]; a[0] = 0; a[n_] := etr[etr[a]][n-1]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, May 28 2013, 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([0], v)} \\ Andrew Howroyd, May 20 2018
CROSSREFS
KEYWORD
nonn,nice,eigen
AUTHOR
EXTENSIONS
New description from Christian G. Bower, Oct 15 1998
STATUS
approved