OFFSET
0,3
LINKS
M. Bernstein and N. J. A. Sloane, Some Canonical Integer Sequences, (arXiv:0205301v1), May 28 2002. [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]
MAPLE
EulerTrans := proc(p) local b; b := proc(n) option remember; local d, j;
`if`(n=0, 1, add(add(d*p(d), d=numtheory[divisors](j))*b(n-j), j=1..n)/n) end end:
A190905 := EulerTrans(n->n!/iquo(n, 2)!^2): seq( A190905(n), n=0..30); # After Alois P. Heinz, A000335.
MATHEMATICA
sf[n_] := With[{f = Floor[n/2]}, Pochhammer[f+1, n-f]/f!]; EulerTrans[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 = EulerTrans[sf]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jul 29 2013, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jul 06 2011
STATUS
approved