The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A131525 Number of degree-2n permutations such that number of cycles of size 2k is odd (or zero) and number of cycles of size 2k-1 is even (or zero), for every k. 1
 1, 2, 13, 371, 17389, 1369057, 168362459, 28396593031, 6237698137129, 1823043651343241, 654314519766396223, 288203550242534470051, 151792464548141462268029, 95104739612472479469277141, 68849533918239714802762113739, 58193958459903387205593351715847 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..220 FORMULA E.g.f.: Product(1+sinh(x^(2*k)/(2*k)),k=1..infinity)*Product(cosh(x^(2*k-1)/(2*k-1)),k=1..infinity). a(n) ~ c * 4^n * n! * (n-1)!, where c = 0.474431... - Vaclav Kotesovec, Jul 21 2019 EXAMPLE a(2)=13 because we have (1)(2)(3)(4), six permutations of type (p)(q)(rs) and six permutations of type (pqrs). MAPLE g:=product((1+sinh(x^(2*k)/(2*k)))*cosh(x^(2*k-1)/(2*k-1)), k=1..25): gser:= series(g, x=0, 30): seq(factorial(2*n)*coeff(gser, x, 2*n), n=0..13); # Emeric Deutsch, Sep 04 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+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(2*n\$2): seq(a(n), n=0..20); # Alois P. Heinz, Mar 09 2015 MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[If[j == 0 || Mod[i + j, 2] == 1, multinomial[n, {n - i j} ~Join~ Table[i, {j}]] (i - 1)!^j/j! b[n - i j, i - 1], 0], {j, 0, n/i}]]]; a[n_] := b[2n, 2n]; a /@ Range[0, 20] (* Jean-François Alcover, Nov 19 2020, after Alois P. Heinz *) CROSSREFS Cf. A130639, A130644. Sequence in context: A075620 A336188 A348015 * A082751 A120935 A015183 Adjacent sequences: A131522 A131523 A131524 * A131526 A131527 A131528 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Aug 25 2007 EXTENSIONS More terms from Emeric Deutsch, Sep 04 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 28 12:56 EDT 2023. Contains 365735 sequences. (Running on oeis4.)