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Search: id:A059419
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| A059419 |
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Triangle T(n,k) (1<=k<=n) of tangent numbers, read by rows: T(n,k) = coefficient of x^n/n! in expansion of (tan x)^k/k!. |
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+0
11
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| 1, 0, 1, 2, 0, 1, 0, 8, 0, 1, 16, 0, 20, 0, 1, 0, 136, 0, 40, 0, 1, 272, 0, 616, 0, 70, 0, 1, 0, 3968, 0, 2016, 0, 112, 0, 1, 7936, 0, 28160, 0, 5376, 0, 168, 0, 1, 0, 176896, 0, 135680, 0, 12432, 0, 240, 0, 1, 353792, 0, 1805056, 0, 508640, 0, 25872, 0, 330, 0, 1, 0
(list; table; graph; listen)
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OFFSET
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1,4
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 259.
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FORMULA
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T(n+1, k) = T(n, k-1) + k*(k+1)*T(n, k+1), T(n, n) = 1.
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EXAMPLE
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1; 0,1; 2,0,1; 0,8,0,1; 16,0,20,0,1; ...
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PROGRAM
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(PARI) T(n, k)=if(k<1|k>n, 0, n!*polcoeff(tan(x+x*O(x^n))^k/k!, n))
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CROSSREFS
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Diagonals give A000182, A024283, A059420 (interspersed with 0's), also A007290, A059421. Row sums give A006229. Essentially the same triangle as A008308.
A111593 (signed triangle with extra column k=0 and row n=0).
Sequence in context: A095403 A011328 A048277 this_sequence A049218 A022902 A037273
Adjacent sequences: A059416 A059417 A059418 this_sequence A059420 A059421 A059422
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KEYWORD
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nonn,easy,nice,tabl
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AUTHOR
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njas, Jan 30 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Feb 01 2001
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