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URL: https://oeis.org/A092923

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A092923
Number of permutations containing exactly one occurrence of the pattern #, with # one of {1-23, 3-21, 12-3, 32-1}.
2
1, 7, 39, 211, 1168, 6728, 40561, 256297, 1696707, 11752973, 85047284, 641782220, 5041634549, 41160207335, 348664792199, 3059885806071, 27781291314396, 260599397789924, 2522492941426381, 25166308238897929, 258507111338795491, 2731176458973448817
OFFSET
3,2
LINKS
Anders Claesson and Toufik Mansour, Counting occurrences of a pattern of type (1,2) or (2,1) in permutations, arXiv:math/0110036 [math.CO], 2001.
FORMULA
G.f.: Sum_{n>=1} (x/(1-n*x)) * Sum_{k>=0} k*x^(k+n)/Product_{l=1..k+n} (1-l*x).
Recurrence: a(n) = 2a(n-1) + Sum_{k=0..n-3} C(n-2, k)*(a(k+1) + B(k+1)), with B(n) the Bell numbers A000110(n).
MATHEMATICA
a[n_ /; n<3] = 0; a[n_] := a[n] = 2 a[n-1] + Sum[Binomial[n-2, k] (a[k+1] + BellB[k+1]), {k, 0, n-3}];
Table[a[n], {n, 3, 24}] (* Jean-François Alcover, Aug 19 2018 *)
PROG
(PARI) a(n)=if(n<1, 0, 2*a(n-1)+sum(k=0, n-3, binomial(n-2, k)*(a(k+1)+polcoeff(serlaplace(exp(exp(x)-1)), k+1))))
CROSSREFS
Column k=1 of A260665.
Sequence in context: A099460 A246987 A322876 * A164550 A125786 A287809
KEYWORD
nonn,changed
AUTHOR
Ralf Stephan, Apr 18 2004
STATUS
approved