

A048099


Number of degreen even permutations of order exactly 2.


17



0, 0, 0, 3, 15, 45, 105, 315, 1323, 5355, 18315, 63855, 272415, 1264263, 5409495, 22302735, 101343375, 507711375, 2495918223, 11798364735, 58074029055, 309240315615, 1670570920095, 8792390355903, 46886941456575, 264381946998975, 1533013006902975, 8785301059346175, 50439885753378303
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OFFSET

1,4


LINKS

Table of n, a(n) for n=1..29.
Koda, Tatsuhiko; Sato, Masaki; Takegahara, Yugen; 2adic properties for the numbers of involutions in the alternating groups, J. Algebra Appl. 14 (2015), no. 4, 1550052 (21 pages).


FORMULA

a(n) = (A001189(n) + A051684(n))/2.
a(n) = Sum_{i=1..floor(n/4)} binomial(n,4i)(4i)!/(2^(2i)(2i)!).  Luis Manuel Rivera Martínez, May 16 2018


MATHEMATICA

Table[Sum[Binomial[n , 4 i] (4 i)!/(2^(2 i) (2 i)!), {i, 1, Floor[n/4]}], {n, 1, 22}](* Luis Manuel Rivera Martínez, May 16 2018 *)


PROG

(PARI) a(n) = sum(i=1, n\4, binomial(n, 4*i)*(4*i)!/(2^(2*i)*(2*i)!)); \\ Michel Marcus, May 17 2018


CROSSREFS

Cf. A001189, A051695. A column of A057740.
Sequence in context: A112810 A094191 A050534 * A030505 A301632 A074355
Adjacent sequences: A048096 A048097 A048098 * A048100 A048101 A048102


KEYWORD

easy,nonn


AUTHOR

Vladeta Jovovic


STATUS

approved



