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Search: id:A073767
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| A073767 |
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Bateman polynomial values n!Z_n(-1). |
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+0
2
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| 1, 3, 20, 188, 2214, 30922, 495816, 8931960, 177999366, 3878476418, 91558971096, 2324529942088, 63084714688540, 1820757355281828, 55645592361311504, 1794034726184859120, 60817844748284215110, 2161623389394872099250
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OFFSET
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0,2
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REFERENCES
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M. C. Fasenmyer, A note on pure recurrence relations, Amer. Math. Monthly 56, (1949), 14-17. Math. Rev. 10,704b.
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FORMULA
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a(n)=n!(Sum k=0..n (n+k)!/(k!^3(n-k)!)) = n!F(-n, n+1;1, 1;-1).
n(2n-3)a(n)=(2n-1)(3n^2-2n-4)a(n-1)-(2n-3)(3n^2-10n+4)(n-1)a(n-2)+(n-1)(2n-1)(n-2)^3a(n-3).
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PROGRAM
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(PARI) a(n)=if(n<0, 0, n!*sum(k=0, n, (n+k)!/(n-k)!/k!^3))
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CROSSREFS
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Cf. A073768.
Adjacent sequences: A073764 A073765 A073766 this_sequence A073768 A073769 A073770
Sequence in context: A129840 A085390 A065980 this_sequence A108206 A120485 A087152
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Aug 08 2002
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