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A291897
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Numerator of E(2*n-1,n), where E(n,x) is the Euler polynomial.
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7
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1, 9, 125, 32977, 971919, 358472059, 47622059953, 137818710619425, 8141400285401267, 9740358918723188381, 3597069206174040366021, 12859671622917809034800123, 3419734700063005545155284375, 8538628250545609672426471056711, 6181704419438256867205044161777369
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OFFSET
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1,2
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COMMENTS
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Conjecture: a(n) is divisible by (2*n-1)^2.
Note that sometimes a(n) is divisible by (2n-1)^3, for example, for n = 1,3,7,9,... when 2*n-1 = 1,5,13,17,... .
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REFERENCES
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M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, Ch. 23.
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LINKS
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FORMULA
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a(n) = (E(2*n-1,n) + (-1)^(n-1)*E(2*n-1,0))*A006519(2*n) + A002425(n).
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MAPLE
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A291897 := n -> euler(2*n-1, n)*2^(padic[ordp](2*n, 2)):
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MATHEMATICA
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f[n_] := Numerator@ EulerE[2 n - 1, n]; Array[f, 15] (* Robert G. Wilson v, Sep 22 2017 *)
Table[2^IntegerExponent[2n, 2] EulerE[2 n-1, n], {n, 1, 15}] (* Peter Luschny, Sep 22 2017 *)
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PROG
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(PARI) a(n) = numerator(subst(eulerpol(2*n-1, 'x), 'x, n)); \\ Michel Marcus, Sep 21 2021
(Python)
from sympy import euler
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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