cp's OEIS Frontend

A370653 Number of permutations of [n] having exactly three adjacent 4-cycles.

%I A370653 #15 Feb 24 2024 11:03:11
%S A370653 0,0,0,0,0,0,0,0,0,0,0,0,1,4,20,120,836,6700,60360,603960,6646090,
%T A370653 79773180,1037232420,14523065760,217865924620,3486094113460,
%U A370653 59266711626080,1066844378466720,20270696788641635,405424394055173080,8514090075293512920
%N A370653 Number of permutations of [n] having exactly three adjacent 4-cycles.
%H A370653 R. A. Brualdi and Emeric Deutsch, <a href="http://arxiv.org/abs/1005.0781">Adjacent q-cycles in permutations</a>, arXiv:1005.0781 [math.CO], 2010.
%F A370653 G.f.: (1/6) * Sum_{k>=3} k! * x^(k+9) / (1+x^4)^(k+1).
%F A370653 a(n) = (1/6) * Sum_{k=0..floor(n/4)-3} (-1)^k * (n-3*k-9)! / k!.
%o A370653 (PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], Vec(sum(k=3, N, k!*x^(k+9)/(1+x^4)^(k+1))/6))
%o A370653 (PARI) a(n, k=3, q=4) = sum(j=0, n\q-k, (-1)^j*(n-(q-1)*(j+k))!/j!)/k!;
%Y A370653 Column k=3 of A177252.
%Y A370653 Cf. A370529, A370530.
%K A370653 nonn
%O A370653 0,14
%A A370653 _Seiichi Manyama_, Feb 24 2024