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A086226
Number of permutations of length n containing exactly one occurrence of the pattern 1-32.
1
0, 0, 1, 9, 73, 637, 6220, 68414, 844067, 11589987, 175612351, 2912695193, 52502754076, 1022091626496, 21372127906257, 477737240288353, 11368449905784189, 286935157928114989, 7656210527253978232
OFFSET
0,4
LINKS
A. Claesson and T. Mansour, Counting Occurrences of a Pattern of Type (1,2) or (2,1) in Permutations, Advances in Applied Mathematics, 29 (2002), 293-310.
FORMULA
a(0)=0; a(n)=a(n-1)+Sum_{k=1..n-1} binomial(n, k)*a(k)+binomial(n-1, k-1)*B(k) where B(k) is the k-th Bell number.
MATHEMATICA
A086226[n_] := A086226[n] = If[n==0, 0, A086226[n-1] + Sum[Binomial[n, k] A086226[k] + Binomial[n-1, k-1] BellB[k], {k, n-1}]];
Array[A086226, 25, 0] (* Paolo Xausa, Jan 09 2024 *)
PROG
(PARI) B(n)=round(exp(-1)*sum(k=0, 200, k^n/k!));
an=vector(100); a(n)=if(n<1, 0, an[n]);
for(n=1, 30, an[n]=a(n-1)+sum(k=1, n-1, binomial(n, k)*a(k)+binomial(n-1, k-1)*B(k)));
an
CROSSREFS
Cf. A000110 (Bell numbers).
Sequence in context: A343353 A121246 A365774 * A338677 A199677 A197676
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Aug 28 2003
STATUS
approved