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A130278 Number of degree-n permutations such that number of cycles of size 2k-1 is odd (or zero) for every k. 1
1, 1, 1, 6, 17, 100, 529, 3766, 31121, 276984, 2755553, 29665306, 364627801, 4639937380, 64952094401, 973467571350, 15750475301921, 264870218828656, 4759194994114369, 90124395399063730, 1812001488739061417, 37956199941196210716, 832297726351555617569 (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.: 1/sqrt(1-x^2)*Product_{k>0} (1+sinh(x^(2*k-1)/(2*k-1))).

EXAMPLE

a(4)=17 because only the following 7 permutations do not qualify: (1)(2)(3)(4), (1)(2)(34), (1)(23)(4), (1)(24)(3), (12)(3)(4), (13)(2)(4) and (14)(2)(3).

MAPLE

g:=(product(1+sinh(x^(2*k-1)/(2*k-1)), k=1..30))/sqrt(1-x^2): gser:=series(g, x =0, 25): seq(factorial(n)*coeff(gser, x, n), n=0..20); # 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)=0 or 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_List] := n!/Times @@ (k!); b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[If[j == 0 || Mod[i, 2] == 0 || 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, Dec 22 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A003483, A006950, A015128, A102759, A130126, A131942, A130219-A130223.

Sequence in context: A219294 A338747 A154494 * A024080 A099436 A209482

Adjacent sequences:  A130275 A130276 A130277 * A130279 A130280 A130281

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 06 2007

EXTENSIONS

More terms from Emeric Deutsch, Aug 24 2007

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)