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%I #15 Feb 19 2024 03:10:00
%S 0,0,0,1,2,11,63,415,3121,26402,248429,2575936,29198926,359351878,
%T 4773277246,68078349863,1037820312090,16842621113247,289946286959875,
%U 5277826030457339,101291053229162471,2044252472193005928,43283094591188747415,959369370636209414390
%N 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.
%H Alois P. Heinz, <a href="/A370392/b370392.txt">Table of n, a(n) for n = 0..450</a>
%F a(n) = A132647(n) - A002628(n).
%F G.f.: Sum_{k>=0} k! * x^k * ( ((1-x^3)/(1-x^4))^k - ((1-x^2)/(1-x^3))^k ).
%o (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))))
%Y Column k=3 of A184182.
%Y Cf. A002628, A132647.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Feb 17 2024
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