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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.
2
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
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.
Sequence in context: A188648 A114175 A080049 * A126745 A362799 A179120
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 17 2024
STATUS
approved