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A263753
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Triangle read by rows: T(n,k) (n>=0, k>=0) is the number of permutations of n with sum of descent tops equal to k.
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3
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1, 1, 1, 0, 1, 1, 0, 1, 3, 0, 1, 1, 0, 1, 3, 7, 1, 3, 7, 0, 1, 1, 0, 1, 3, 7, 16, 3, 14, 17, 32, 3, 7, 15, 0, 1, 1, 0, 1, 3, 7, 16, 34, 14, 32, 69, 72, 129, 32, 68, 70, 118, 7, 15, 31, 0, 1, 1, 0, 1, 3, 7, 16, 34, 77, 32, 100, 149, 274, 292, 496, 220, 388, 536
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OFFSET
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0,9
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COMMENTS
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LINKS
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EXAMPLE
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Triangle begins:
1;
1;
1,0,1;
1,0,1,3,0,1;
1,0,1,3,7,1,3,7,0,1;
1,0,1,3,7,16,3,14,17,32,3,7,15,0,1;
1,0,1,3,7,16,34,14,32,69,72,129,32,68,70,118,7,15,31,0,1;
...
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MAPLE
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b:= proc(s) option remember; (n-> `if`(n=0, 1, expand(
add(b(s minus {j})*`if`(j<n, x^n, 1), j=s))))(nops(s))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b({$1..n})):
seq(T(n), n=0..9); # Alois P. Heinz, Oct 25 2015, revised, Jan 31 2023
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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One term prepended and one term corrected by Alois P. Heinz, Oct 25 2015
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STATUS
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approved
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