A370392 Number of permutations of [n] whose longest block is of length 3. A block of a permutation is a maximal sequence of consecutive integers which appear in consecutive positions.

0, 0, 0, 1, 2, 11, 63, 415, 3121, 26402, 248429, 2575936, 29198926, 359351878, 4773277246, 68078349863, 1037820312090, 16842621113247, 289946286959875, 5277826030457339, 101291053229162471, 2044252472193005928, 43283094591188747415, 959369370636209414390

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Formula

a(n) = A132647(n) - A002628(n).

G.f.: Sum_{k>=0} k! * x^k * ( ((1-x^3)/(1-x^4))^k - ((1-x^2)/(1-x^3))^k ).

Prog

(PARI) my(N=30, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=0, N, k!*x^k*(((1-x^3)/(1-x^4))^k-((1-x^2)/(1-x^3))^k))))

Crossrefs

Column k=3 of A184182.

Cf. A002628, A132647.

Sequence in context: A188648 A114175 A080049 * A126745 A362799 A179120

Adjacent sequences: A370389 A370390 A370391 * A370393 A370394 A370395

Keyword

nonn

Author

Seiichi Manyama, Feb 17 2024

Status

approved