A370384 Number of permutations of [n] having no substring [k,k+1,k+2,k+3,k+4,k+5].
1, 1, 2, 6, 24, 120, 719, 5037, 40306, 362802, 3628296, 39913080, 478970641, 6226733531, 87175347936, 1307641346772, 20922387099240, 355682119243320, 6402298503373917, 121643960874649867, 2432883613692550316, 51090627024035616300, 1123995015882951892680
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..450
- D. M. Jackson and R. C. Read, A note on permutations without runs of given length, Aequationes Math. 17 (1978), no. 2-3, 336-343.
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*((x-x^6)/(1-x^6))^k))
Formula
G.f.: Sum_{k>=0} k! * ( (x-x^6)/(1-x^6) )^k.
a(n) = Sum_{k=0..5} A184182(n,k). - Alois P. Heinz, Feb 17 2024