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

0,3

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.

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*((x-x^6)/(1-x^6))^k))

Crossrefs

Cf. A000255, A002628, A132647, A184182, A370383.

Sequence in context: A297204 A071088 A177533 * A122417 A321008 A033644

Adjacent sequences: A370381 A370382 A370383 * A370385 A370386 A370387

Keyword

nonn

Author

Seiichi Manyama, Feb 17 2024

Status

approved