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Search: id:A051396
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| A051396 |
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a(n) = (2*n-2)*(2*n-3)*a(n-1)+1. |
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+0
3
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| 0, 1, 3, 37, 1111, 62217, 5599531, 739138093, 134523132927, 32285551902481, 9879378882159187, 3754163975220491061, 1734423756551866870183, 957401913616630512341017, 622311243850809833021661051, 470467300351212233764375754557, 409306551305554643375006906464591
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The sequence 1,0,3,0,37,... has e.g.f. cosh(x)/(1-x^2) with a(n)=sum{k=0..n, C(n,k)k!(1+(-1)^k)(1+(-1)^(n-k))/4}. - Paul Barry (pbarry(AT)wit.ie), May 01 2005
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REFERENCES
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A. Petojevic, On Kurepa's Hypothesis for the Left Factorial, FILOMAT (Nis), 12:1 (1998), p. 29-37.
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FORMULA
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a(n) = Sum_{k=0..n-1} (2*n-2)!/(2*k)! = floor((2*n-2)!*cosh(1)), n>=1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 10 2002
a(n+1)=sum{k=0..2n, C(2n, k)*k!*(1+(-1)^k)^2}; - Paul Barry (pbarry(AT)wit.ie), May 01 2005
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MAPLE
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A051396 := proc(n) option remember; if n <= 1 then n else (2*n-2)*(2*n-3)*A051396(n-1)+1; fi; end;
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CROSSREFS
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Bisection of abs(A009179(n)).
Sequence in context: A054596 A003717 A003716 this_sequence A113074 A128083 A132931
Adjacent sequences: A051393 A051394 A051395 this_sequence A051397 A051398 A051399
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KEYWORD
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nonn
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AUTHOR
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Aleksandar Petojevic.
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