A370383 Number of permutations of [n] having no substring [k,k+1,k+2,k+3,k+4].
1, 1, 2, 6, 24, 119, 717, 5026, 40242, 362376, 3625081, 39885851, 478714416, 6224078292, 87145277160, 1307271652917, 20917481850667, 355612235468396, 6401234296266540, 121626707638142280, 2432586885636105251, 51085230669413519349, 1123891538655073251190
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^5)/(1-x^5))^k))
Formula
G.f.: Sum_{k>=0} k! * ( (x-x^5)/(1-x^5) )^k.
a(n) = Sum_{k=0..4} A184182(n,k). - Alois P. Heinz, Feb 17 2024