A339058 a(n) = 4^n*Euler(n, 1/4)*2^(valuation_{2}(n + 1)).
1, -2, -3, 44, 57, -722, -2763, 196888, 250737, -5746082, -36581523, 2049374444, 7828053417, -259141449842, -2309644635483, 705775346640176, 898621108880097, -38901437271432002, -445777636063460643, 43136210244502819244, 274613643571568682777, -14685255919931552812562
Offset: 0
Keywords
Examples
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] ...
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..432
Crossrefs
Programs
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Maple
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
Array[4^#*EulerE[#, 1/4]*2^IntegerExponent[# + 1, 2] &, 22, 0] (* Michael De Vlieger, Mar 15 2022 *)
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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)])