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A130644 Number of degree-2n permutations without odd cycles and such that number of cycles of size 2k is odd (or zero) for every k. 2
1, 1, 6, 225, 8400, 760725, 91725480, 15563633085, 3381661483200, 1015992072520425, 360153767651277600, 160068908768727783825, 84298688029883001074400, 53051020433282263735468125, 38316864396320965168213500000, 32660810942813910822645908353125 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
E.g.f.: Product_{k>0} (1+sinh(x^(2*k)/(2*k))).
EXAMPLE
a(2)=6 because we have (1234),(1243),(1324),(1342),(1423) and (1432).
MAPLE
g:=product(1+sinh(x^(2*k)/(2*k)), k=1..50): gser:=series(g, x=0, 44): seq(factorial(2*n)*coeff(gser, x, 2*n), n=0..14); # 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 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(2*n$2):
seq(a(n), n=0..20); # 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] == 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[2n, 2n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 08 2017, after Alois P. Heinz *)
CROSSREFS
Cf. A060307.
Sequence in context: A061610 A054324 A117255 * A223100 A233142 A166502
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 April 13 10:11 EDT 2024. Contains 371640 sequences. (Running on oeis4.)