A370392 - OEIS

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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

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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.