OFFSET
1,3
COMMENTS
Zero together with the absolute values of this sequence give A330373. - Omar E. Pol, Dec 31 2019
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..500
FORMULA
a(n) = n*A081362(n) for n >= 1.
G.f.: x*f'(x), where f(x) = Product_{k > 0} (1 - x^(2*k - 1)).
a(n) ~ (-1)^n * exp(Pi*sqrt(n/6)) * n^(1/4) / (2^(7/4) * 3^(1/4)). - Vaclav Kotesovec, Nov 21 2016
EXAMPLE
There are 12 partitions of 8 into an even number of parts and 10 into an odd number of parts, so that a(8) = 12*8 - 10*8 = 16.
MATHEMATICA
Table[n*SeriesCoefficient[Product[1-x^k, {k, 1, n, 2}], {x, 0, n}], {n, 70}]
nmax = 60; Rest[CoefficientList[Series[x*D[Product[1/(1 + x^k), {k, 1, nmax}], x], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Nov 21 2016 *)
PROG
(PARI) a(n)= my(A); n*if(n<0, 0, A= x*O(x^n); polcoeff(eta(x+A)/eta(x^2+A), n));
vector(50, n, a(n) ) /* from Michael Somos code in A081362 */ \\ G. C. Greubel, Dec 31 2019
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Clark Kimberling, Mar 27 2014
STATUS
approved