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A130276
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Number of degree-2n permutations such that number of cycles of size 2k-1 is even (or zero) for every k.
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0
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1, 2, 16, 416, 20224, 1645312, 196388864, 33279311872, 7427338829824, 2151276556845056, 771086221948223488, 340572557390992900096, 179222835344084459061248, 112158801651454395931426816
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| E.g.f. with interleaved zeros: 1/sqrt(1-x^2)*Product_{k>=1} cosh(x^(2*k-1)/(2*k-1)).- Geoffrey Critzer, Jan 02 2011
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EXAMPLE
| a(2)=16 because there are 8 permutations that do not qualify: (1)(234), (1)(243), (123)(4), (124)(3), (132)(4), (134)(2), (142)(3) and (143)(2).
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MAPLE
| g:=(product(cosh(x^(2*k-1)/(2*k-1)), k=1..30))/sqrt(1-x^2): gser:=series(g, x= 0, 30): seq(factorial(2*n)*coeff(gser, x, 2*n), n=0..13); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007
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PROG
| (PARI) N=31; x='x+O('x^N);
v0=Vec(serlaplace(1/sqrt(1-x^2)*prod(k=1, N, cosh(x^(2*k-1)/(2*k-1)))));
vector(#v0\2, n, v0[2*n-1]) \\ Joerg Arndt, Jan 03 2011
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CROSSREFS
| Cf. A003483, A006950, A015128, A102759, A130126, A131942, A130219-A130223.
Sequence in context: A188904 A189104 A181213 * A027871 A009397 A009700
Adjacent sequences: A130273 A130274 A130275 * A130277 A130278 A130279
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KEYWORD
| easy,nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06 2007
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007
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