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A339058
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a(n) = 4^n*Euler(n, 1/4)*2^(valuation_{2}(n + 1)).
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2
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1, -2, -3, 44, 57, -722, -2763, 196888, 250737, -5746082, -36581523, 2049374444, 7828053417, -259141449842, -2309644635483, 705775346640176, 898621108880097, -38901437271432002, -445777636063460643, 43136210244502819244, 274613643571568682777, -14685255919931552812562
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OFFSET
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0,2
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LINKS
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EXAMPLE
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The array of the general case starts:
[k]
[1] 1, 1, 0, -1, 0, 1, 0, -17, 0, ... [A198631]
[2] 1, 0, -1, 0, 5, 0, -61, 0, 1385, ... [A122045]
[3] 1, -1, -2, 13, 22, -121, -602, 18581, 30742, ... [A156179]
[4] 1, -2, -3, 44, 57, -722, -2763, 196888, 250737, ... [this sequence]
[5] 1, -3, -4, 99, 116, -2523, -8764, 1074243, 1242356, ... [A156182]
...
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MAPLE
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a := n -> 4^n*euler(n, 1/4)*2^padic[ordp](n+1, 2): seq(a(n), n=0..9);
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MATHEMATICA
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Array[4^#*EulerE[#, 1/4]*2^IntegerExponent[# + 1, 2] &, 22, 0] (* Michael De Vlieger, Mar 15 2022 *)
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PROG
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(SageMath)
def euler_sum(n):
return (-1)^n*sum(2^k*binomial(n, k)*euler_number(k) for k in (0..n))
def a(n): return euler_sum(n) << valuation(n + 1, 2)
print([a(n) for n in range(22)])
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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