|
| |
|
|
A130278
|
|
Number of degree-n permutations such that number of cycles of size 2k-1 is odd (or zero) for every k.
|
|
0
| |
|
|
1, 1, 1, 6, 17, 100, 529, 3766, 31121, 276984, 2755553, 29665306, 364627801, 4639937380, 64952094401, 973467571350, 15750475301921, 264870218828656, 4759194994114369, 90124395399063730, 1812001488739061417
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
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 (deutsch(AT)duke.poly.edu), Aug 24 2007
|
|
|
CROSSREFS
| Cf. A003483, A006950, A015128, A102759, A130126, A131942, A130219-A130223.
Sequence in context: A123189 A047156 A154494 * A024080 A099436 A077022
Adjacent sequences: A130275 A130276 A130277 * A130279 A130280 A130281
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 06 2007
|
|
|
EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 24 2007
|
| |
|
|
