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%I #10 Feb 26 2017 10:51:56
%S 1,4,57,4480,866460,302835456,165589522560,130247609057280,
%T 139297568464454400,194428045753727385600,343266731083210449715200,
%U 747889980460943180326502400,1971026081420013638259189350400,6180432779330984921337015828480000
%N Number of endofunctions on [2n] whose cycle lengths are multiples of n.
%H Alois P. Heinz, <a href="/A246618/b246618.txt">Table of n, a(n) for n = 0..195</a>
%F a(n) = A246609(2n,n).
%F a(n) ~ 2^(3*n-1/2) * n^(2*n-1) / exp(n). - _Vaclav Kotesovec_, Sep 01 2014
%p with(combinat):
%p b:= proc(n, i, k) option remember; `if`(n=0, 1,
%p `if`(i=0 or i>n, 0, add(b(n-i*j, i+k, k)*(i-1)!^j*
%p multinomial(n, n-i*j, i$j)/j!, j=0..n/i)))
%p end:
%p a:= n->add(b(j, n$2)*(2*n)^(2*n-j)*binomial(2*n-1, j-1), j=0..2*n):
%p seq(a(n), n=0..15);
%t multinomial[n_, k_] := n!/Times @@ (k!); b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0 || i > n, 0, Sum[b[n - i*j, i + k, k]*(i - 1)!^j * multinomial[n, Join[{n-i*j}, Array[i&, j]]]/j!, {j, 0, n/i}]]]; a[0] = 1; a[n_] := Sum[b[j, n, n]*(2n)^(2n-j)*Binomial[2n-1, j-1], {j, 0, 2n}]; Table[a[n], {n, 0, 15}] (* _Jean-François Alcover_, Feb 26 2017, after _Alois P. Heinz_ *)
%Y Cf. A246609.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Aug 31 2014
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