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 A060307 Number of degree-4n permutations without odd cycles and such that number of cycles of size 2k is even (or zero) for every k. 5
 1, 3, 1365, 8534295, 204893714025, 15735481638151275, 2760485970394430603325, 1006427270776555103089989375, 659316841888260316767029819420625, 740198799422691022278446846884066321875, 1306298536067264588818106780684613899555353125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..100 FORMULA E.g.f.: Product_{k >= 1} cosh x^(2k)/(2k). MAPLE 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)=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(4*n\$2): seq(a(n), n=0..15); # Alois P. Heinz, Mar 09 2015 MATHEMATICA nn = 40; Select[Range[0, nn]! CoefficientList[Series[Product[Cosh[x^(2 i)/(2 i)], {i, 1, nn}], {x, 0, nn}], x], # > 0 &] (* Geoffrey Critzer, Jan 16 2012 *) CROSSREFS Cf. A003483. Cf. A013302. Sequence in context: A122389 A036066 A262516 * A119111 A233195 A219783 Adjacent sequences: A060304 A060305 A060306 * A060308 A060309 A060310 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, Mar 28 2001, Aug 10 2007 STATUS approved

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Last modified May 25 16:13 EDT 2024. Contains 372800 sequences. (Running on oeis4.)