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A370426 Number of permutations of [n] having exactly two adjacent 2-cycles. 5
0, 0, 0, 0, 1, 3, 9, 48, 306, 2190, 17810, 162480, 1642635, 18231465, 220420179, 2883693792, 40592133316, 611765693532, 9828843229764, 167702100599520, 3028466654021205, 57708568527002415, 1157199837194069405, 24358905149602459920, 537053113128448187766 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
R. A. Brualdi and Emeric Deutsch, Adjacent q-cycles in permutations, arXiv:1005.0781 [math.CO], 2010.
FORMULA
G.f.: (1/2) * Sum_{k>=2} k! * x^(k+2) / (1+x^2)^(k+1).
a(n) = (1/2) * Sum_{k=0..floor(n/2)-2} (-1)^k * (n-k-2)! / k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(sum(k=2, N, k!*x^(k+2)/(1+x^2)^(k+1))/2))
(PARI) a(n, k=2, q=2) = sum(j=0, n\q-k, (-1)^j*(n-(q-1)*(j+k))!/j!)/k!;
CROSSREFS
Column k=2 of A177248.
Sequence in context: A306947 A183952 A298308 * A141051 A001530 A316449
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 21 2024
STATUS
approved

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Last modified June 15 10:19 EDT 2024. Contains 373407 sequences. (Running on oeis4.)