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

0,2

Links

Michael De Vlieger, Table of n, a(n) for n = 0..432

Example

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]
...

Maple

a := n -> 4^n*euler(n, 1/4)*2^padic[ordp](n+1, 2): seq(a(n), n=0..9);

Mathematica

Array[4^#*EulerE[#, 1/4]*2^IntegerExponent[# + 1, 2] &, 22, 0] (* Michael De Vlieger, Mar 15 2022 *)

Prog

(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)])

Crossrefs

Cf. A198631, A122045, A156179, A156182, A156191, A339057.

Note the difference from A001586, A188458, and A212435.

Sequence in context: A356047 A042819 A218002 * A356565 A255969 A329945

Adjacent sequences: A339055 A339056 A339057 * A339059 A339060 A339061

Keyword

sign

Author

Peter Luschny, Nov 27 2020

Status

approved