A370390 Number of permutations of [n] whose longest block is of length 2. A block of a permutation is a maximal sequence of consecutive integers which appear in consecutive positions.

0, 0, 1, 2, 10, 53, 334, 2428, 20009, 184440, 1881050, 21034905, 255967940, 3367720736, 47641219569, 721160081974, 11631770791362, 199159952915293, 3607908007376418, 68946510671942892, 1386140583681969289, 29247292475233307612, 646231776371742321826

Offset

0,4

Links

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

Formula

a(n) = A002628(n) - A000255(n-1).

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

Prog

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

Crossrefs

Column k=2 of A184182.

Cf. A000255, A002628.

Sequence in context: A037619 A221610 A247102 * A009320 A204186 A009322

Adjacent sequences: A370387 A370388 A370389 * A370391 A370392 A370393

Keyword

nonn

Author

Seiichi Manyama, Feb 17 2024

Status

approved