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Search: id:A085734
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| A085734 |
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Triangle read by rows: T(0,0) = 1, T(n,k) = sum(j=max(0,1-k) to n-k, (2^j)*(C(k+j,1+j) + C(k+j+1,1+j))*T(n-1,k-1+j)). |
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+0
4
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| 1, 2, 3, 16, 30, 15, 272, 588, 420, 105, 7936, 18960, 16380, 6300, 945, 353792, 911328, 893640, 429660, 103950, 10395, 22368256, 61152000, 65825760, 36636600, 11351340, 1891890, 135135, 1903757312, 5464904448, 6327135360, 3918554640
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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A triangle related to Euler numbers and tangent numbers.
T(n,k) = number of down-up permutations on [2n+2] with k+1 left-to-right maxima. For example, T(1,1) counts the following 3 down-up permutations on [4] each with 2 left-to-right maxima: 2143, 3142, 3241. - David Callan (callan(AT)stat.wisc.edu), Oct 25 2004
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REFERENCES
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Ghislain R. Franssens, On a Number Pyramid Related to the Binomial, Deleham, Eulerian, MacMahon and Stirling number triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.1.
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FORMULA
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T(n, k) = A083061(n, k)*2^(n-k) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 27 2005
E.g.f.: sec(x)^y. - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 20 2007
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EXAMPLE
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{1}; {2, 3}; {16, 30, 15}; {272, 588, 420, 105}
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CROSSREFS
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T(n, 0) = A000182(n), tangent numbers, T(n, n) = A001147(n+1), sum(k>=0, T(n, k) = A000364(n+1), Euler numbers.
Cf. A088874.
Sequence in context: A074182 A074759 A102882 this_sequence A034382 A034383 A072684
Adjacent sequences: A085731 A085732 A085733 this_sequence A085735 A085736 A085737
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Deleham Philippe (kolotoko(AT)wanadoo.fr), Jul 20 2003
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EXTENSIONS
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Edited and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) Nov 23 2003
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