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Search: id:A008309
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| A008309 |
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Triangle T(n,k) of arctangent numbers: expansion of arctan(x)^n/n!. |
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+0
2
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| 1, 1, -2, 1, -8, 1, 24, -20, 1, 184, -40, 1, -720, 784, -70, 1, -8448, 2464, -112, 1, 40320, -52352, 6384, -168, 1, 648576, -229760, 14448, -240, 1, -3628800, 5360256, -804320, 29568, -330, 1
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 260.
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FORMULA
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E.g.f.: arctan(x)^k/k!=sum {n=0..inf} T(m, [ k+1 ]/2) x^m/m! where m=2n+k%2.
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EXAMPLE
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1; 0,1; -2,0,1; 0,-8,0,1; 24,0,-200,0,1; 0,184,0,-40,0,1; ...
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PROGRAM
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(PARI) T(n, k)=polcoeff(serlaplace(a(2*k-n%2)), n) where a(n)=atan(x)^n/n!
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CROSSREFS
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Essentially same as A049218.
A007290(n)=-T(n, [ (n-1)/2 ]), A010050(n)=(-1)^n*T(2n+1, 1), A049034(n)=(-1)^n*T(2n+2, 1), A049214(n)=(-1)^n*T(2n+3, 2), A049215(n)=(-1)^n*T(2n+4, 2), A049216(n)=(-1)^n*T(2n+5, 3), A049217(n)=(-1)^n*T(2n+6, 3).
Sequence in context: A008308 A118931 A101280 this_sequence A131175 A066532 A020778
Adjacent sequences: A008306 A008307 A008308 this_sequence A008310 A008311 A008312
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KEYWORD
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sign,tabf,nice
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AUTHOR
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njas
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EXTENSIONS
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Additional comments from Michael Somos.
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