A190905 Euler transform of the swinging factorial A056040.

1, 1, 3, 9, 18, 60, 117, 371, 747, 2199, 4697, 12735, 28571, 72815, 169176, 412440, 978086, 2316754, 5547293, 12909723, 30966639, 71357601, 170636159, 391242623, 930120982, 2128073530, 5023630830, 11486060090, 26918052717, 61539213693, 143227189518

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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

Cf. A107895.

Sequence in context: A101652 A026565 A174470 * A133136 A161138 A201222

Adjacent sequences: A190902 A190903 A190904 * A190906 A190907 A190908

Keyword

nonn

Author

Peter Luschny, Jul 06 2011

Status

approved