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A306148
a(n) = numerator(n!*[z^n](z*(exp(z)+2*exp(-(1/2)*z)*cos((1/2)*z* 3^(1/2)))/(1-exp(-z)))).
1
3, 3, 1, 3, 59, 5, 43, 7, 139, 9, -127, 11, 62099, 13, -2513, 15, 278923, 17, -16761307, 19, 13372769, 21, -327211439, 23, 18102814403, 25, -655076773, 27, 1818961119031, 29, -659884043593273, 31, 6494995052521753, 33, -197424183925133, 35, 2015477183184289687757
OFFSET
0,1
FORMULA
a(2*n - 3) = 2*n - 3 for n >= 3.
EXAMPLE
Rational values start: 3, 3/2, 1/2, 3, 59/10, 5, 43/14, 7, 139/10, 9, -127/22, 11, 62099/910, 13, -2513/10, 15, 278923/170, 17, ....
MAPLE
gf := z*(exp(z)+2*exp(-(1/2)*z)*cos((1/2)*z*sqrt(3)))/(1-exp(-z));
ser := series(gf, z, 100): seq(numer(n!*coeff(ser, z, n)), n=0..36);
CROSSREFS
Cf. A306149 (denominator).
Sequence in context: A366556 A275625 A331901 * A106836 A241235 A125607
KEYWORD
sign,frac
AUTHOR
Peter Luschny, Aug 19 2018
STATUS
approved