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 A130648 Number of degree-n permutations without even cycles and such that number of cycles of size 2k-1 is odd (or zero) for every k. 2
 1, 1, 0, 3, 8, 25, 184, 721, 9904, 66753, 691088, 5973121, 84925048, 940427137, 12801319816, 186556383105, 3174772979936, 48489077948161, 842173637012896, 15359492773456129, 316965131969908072, 6368424993521096961, 135098381153771956952, 2980219360336428021505 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..450 FORMULA E.g.f.: Product_{k>0} (1+sinh(x^(2*k-1)/(2*k-1))). EXAMPLE a(3)=3 because we have (1)(2)(3), (123) and (132). MAPLE g:=product(1+sinh(x^(2*k-1)/(2*k-1)), k=1..30): gser:=series(g, x=0, 27): seq(factorial(n)*coeff(gser, x, n), n=0..24); # Emeric Deutsch, Aug 24 2007 # second Maple program: with(combinat): b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(       `if`(j=0 or irem(i, 2)=1 and irem(j, 2)=1, multinomial(n,        n-i*j, i\$j)*(i-1)!^j/j!*b(n-i*j, i-1), 0), j=0..n/i)))     end: a:= n-> b(n\$2): seq(a(n), n=0..30);  # Alois P. Heinz, Mar 09 2015 MATHEMATICA multinomial[n_, k_] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[If[j == 0 || Mod[i, 2] == 1 && Mod[j, 2] == 1, multinomial[n, Join[{n-i*j}, Array[i&, j]]]*(i-1)!^j/j!*b[n-i*j, i-1], 0], {j, 0, n/i}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 08 2017, after Alois P. Heinz *) CROSSREFS Cf. A060307. Sequence in context: A268114 A097713 A009392 * A061812 A009452 A206141 Adjacent sequences:  A130645 A130646 A130647 * A130649 A130650 A130651 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Aug 11 2007 EXTENSIONS More terms from Emeric Deutsch, Aug 24 2007 STATUS approved

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)