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Search: id:A002681
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| A002681 |
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Numerators of coefficients for repeated integration.
(Formerly M5136 N2227)
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+0
2
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| 1, -1, 1, -23, 263, -133787, 157009, -16215071, 2689453969, -26893118531, 5600751928169, -3340626516019229, 885646796787371, -859202038021848149, 2766671664340938282413, -319473088311274492668499, 436677987276721765221113, -191960665849028069896950959123
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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H. E. Salzer, Coefficients for repeated integration with central differences, Journal of Mathematics and Physics, 28 (1949), 54-61.
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FORMULA
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a(n) is the numerator of ((n+1)/2)M(n)+(2n+2)M(n+1), where M(n)=(2/(2n+1)!)*int(t*product(t^2-k^2, k=1..n), t=0..1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 25 2005
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MAPLE
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M:=n->(2/(2*n+1)!)*int(t*product(t^2-k^2, k=1..n), t=0..1): A:=n->((n+1)/2)*M(n)+(2*n+2)*M(n+1): seq(numer(A(n)), n=0..18); (Deutsch)
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CROSSREFS
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Cf. A002195, A002196, A002682.
Adjacent sequences: A002678 A002679 A002680 this_sequence A002682 A002683 A002684
Sequence in context: A042018 A125411 A140620 this_sequence A142220 A142027 A010975
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KEYWORD
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sign,frac
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AUTHOR
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njas
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 25 2005
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