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A246071 Number of endofunctions f on [2n] satisfying f^n(i) = i for all i in [n]. 2
1, 2, 50, 1440, 215760, 11218000, 8859219696, 549669946784, 797599992178688, 195297824029876992, 225830701916170080000, 33538442785393084937728, 478648537323384927696592896, 26649057768458576467019134976, 207869233649005397144301933676544 (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

a(n) = A246070(2n,n).

MAPLE

with(numtheory): with(combinat): M:=multinomial:

b:= proc(n, k, p) local l, g; l, g:= sort([divisors(p)[]]),

      proc(k, m, i, t) option remember; local d, j; d:= l[i];

        `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)$j)/j!*

         (d-1)!^j *M(m, m-t*j, t$j) *g(k-(d-t)*j, m-t*j,

        `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),

        `if`(t=0, [][], m/t))))

      end; g(k, n-k, nops(l), 0)

    end:

a:= n-> `if`(n=0, 1, b(2*n, n$2)):

seq(a(n), n=0..20);

CROSSREFS

Cf. A246070.

Sequence in context: A083941 A080263 A221241 * A088920 A278456 A231043

Adjacent sequences:  A246068 A246069 A246070 * A246072 A246073 A246074

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 12 2014

STATUS

approved

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Last modified October 20 20:04 EDT 2019. Contains 328270 sequences. (Running on oeis4.)