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)))).

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

Links

Table of n, a(n) for n=0..36.

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

Adjacent sequences: A306145 A306146 A306147 * A306149 A306150 A306151

Keyword

sign,frac

Author

Peter Luschny, Aug 19 2018

Status

approved