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A007003 Euler transform of numbers of preferential arrangements. 2
1, 2, 5, 19, 97, 658, 5458, 53628, 606871, 7766312, 110811174, 1743359979, 29972475254, 558940415943, 11235765584497, 242168565186139, 5570683131749362, 136215122718876230, 3527978807819506487, 96480528944412962039, 2778048842021042988465 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..160

N. J. A. Sloane, Transforms

FORMULA

a(n) ~ n! / (2*(log(2))^(n+1)). - Vaclav Kotesovec, Aug 25 2014

MAPLE

with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: f:= proc(n) option remember; local k; if n<=1 then 1 else add(binomial(n, k) *f(n-k), k=1..n) fi end: aa:= etr(k->f(k-1)): a:= n->aa(n+1): seq(a(n), n=0..30); # Alois P. Heinz, Sep 08 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]; f[n_] := f[n] = If[n <= 1, 1, Sum[Binomial[n, k]*f[n-k], {k, 1, n}]]; aa := etr[f[#-1]&]; a[n_] := aa[n+1]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 10 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A000670, A290352.

Sequence in context: A188914 A049984 A052866 * A020117 A054687 A076669

Adjacent sequences:  A007000 A007001 A007002 * A007004 A007005 A007006

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Alois P. Heinz, Sep 08 2008

STATUS

approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)