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Search: id:A046739
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| A046739 |
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Triangle read by rows, related to number of permutations of [n] with 0 successions and k rises. |
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+0
4
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| 0, 1, 1, 1, 1, 7, 1, 1, 21, 21, 1, 1, 51, 161, 51, 1, 1, 113, 813, 813, 113, 1, 1, 239, 3361, 7631, 3361, 239, 1, 1, 493, 12421, 53833, 53833, 12421, 493, 1, 1, 1003, 42865, 320107, 607009, 320107, 42865, 1003, 1, 1, 2025, 141549, 1704693, 5494017
(list; graph; listen)
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OFFSET
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1,6
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REFERENCES
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D. P. Roselle, Permutations by number of rises and successions, Proc. Amer. Math. Soc., 19 (1968), 8-16.
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FORMULA
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a(n+1, r)=r*a(n, r)+(n+1-r)a(n, r-1)+n*a(n-1, r-1).
exp(-t)/(1 - exp((x-1)t)/(x-1)) = 1 + x*t^2/2! + (x+x^2)*t^3/3! + (x+7x^2+x^3)*t^4/4! + (x+21x^2+21x^3+x^4)*t^5/5! + ... - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jun 11 2004
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EXAMPLE
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0; 1; 1 1; 1 7 1; 1 21 21 1; 1 51 161 51 1; ...
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CROSSREFS
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Cf. A046740. Row sums give A000166. Diagonals give A070313, A070315.
Sequence in context: A081580 A082110 A119727 this_sequence A056752 A053714 A033933
Adjacent sequences: A046736 A046737 A046738 this_sequence A046740 A046741 A046742
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KEYWORD
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nonn,easy,nice,tabf
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AUTHOR
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njas
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Apr 07 2000
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