This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A178669 #23 Jun 02 2025 02:58:37
%S A178669 0,3,15,45,315,3150,28350,274050,3014550,36330525,472296825,
%T A178669 6609317715,99139765725,1586293008300,26966981141100,485404420000500,
%U A178669 9222683980009500,184453709062998375
%N A178669 The number of permutations of [n] with 2 cycles of length 2.
%H A178669 Vincenzo Librandi, <a href="/A178669/b178669.txt">Table of n, a(n) for n = 3..200</a>
%F A178669 a(n)=n!*sum_{j=k.. [n/2]} (-1)^j/((j-k)!*2^j*k!). E.g.f. = exp(-z^2/2)*z^(2*k) / ((1-z)*2^k*k!), where k is the number of cycles of length 2.
%F A178669 a(n) ~ n! * exp(-1/2)/8. - _Vaclav Kotesovec_, Mar 20 2014
%e A178669 a(4)=3 counts the 3 permutations (2143), (3412), (4321) with 2 cycles
%e A178669 of length 2
%p A178669 A178669 := proc(n) local k ; k :=2 ; n!*add( (-1)^j/(j-k)!/2^j/k!,j=k..n/2) ; end proc:
%p A178669 seq(A178669(n),n=3..20) ;
%t A178669 d=Exp[-x^2/2]/(1-x); Range[0,20]! CoefficientList[Series[(3x^4/4! )d, {x,0,20}], x] (* _Geoffrey Critzer_, Nov 29 2011 *)
%Y A178669 Cf. A088436 (k=1 cycle), A000266 (k=0 cycle).
%K A178669 nonn
%O A178669 3,2
%A A178669 _Paul Weisenhorn_, Jun 02 2010
%E A178669 Typo in a(18) corrected by _Vincenzo Librandi_, Mar 21 2014