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A131526 Number of degree-n permutations such that number of cycles of size 2k is even (or zero) and number of cycles of size 2k-1 is odd (or zero), for every k. 1
1, 1, 0, 3, 11, 40, 184, 1036, 12949, 88488, 807008, 7362586, 113572183, 1238477032, 15630890560, 228998728050, 4141605806441, 62222251093216, 1030119451142656, 19050688698470434, 412037845709792107, 8102391640556570616, 165794307361686866432 (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(1+sinh(x^(2*k-1)/(2*k-1)), k=1..infinity) *Product(cosh(x^(2*k)/(2*k)), k=1..infinity).

EXAMPLE

a(4)=11 because we have (1)(234), (1)(243), (123)(4), (124)(3), (132)(4), (134)(2), (142)(3), (143)(2), (12)(34), (13)(24) and (14)(23).

MAPLE

g:=(product(1+sinh(x^(2*k-1)/(2*k-1)), k=1..40))*(product(cosh(x^(2*k)/(2*k)), k=1..40)): gser:=series(g, x=0, 25); seq(factorial(n)*coeff(gser, x, n), n=0..21); # Emeric Deutsch, Aug 28 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)=0, 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

CROSSREFS

Cf. A060307, A130648.

Sequence in context: A242467 A149064 A149065 * A329261 A073622 A181863

Adjacent sequences:  A131523 A131524 A131525 * A131527 A131528 A131529

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 25 2007

EXTENSIONS

More terms from Emeric Deutsch, Aug 28 2007

STATUS

approved

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Last modified January 21 13:47 EST 2020. Contains 331113 sequences. (Running on oeis4.)