OFFSET
0,3
COMMENTS
a(n) = A323675(n*(n+1)) for n >= 0.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..70
FORMULA
a(n) = [x^(n*(n+1))] Sum_{n>=0} x^n * (x^n + i)^n / (1 + i*x^(n+1))^(n+1).
a(n) = [x^(n*(n+1))] Sum_{n>=0} x^n * (x^n - i)^n / (1 - i*x^(n+1))^(n+1).
EXAMPLE
Given the g.f. of A323675, G(x) = Sum_{n>=0} x^n * (x^n + i)^n / (1 + i*x^(n+1))^(n+1), i.e.,
G(x) = 1/(1 + i*x) + x*(x + i)/(1 + i*x^2)^2 + x^2*(x^2 + i)^2/(1 + i*x^3)^3 + x^3*(x^3 + i)^3/(1 + i*x^4)^4 + x^4*(x^4 + i)^4/(1 + i*x^5)^5 + x^5*(x^5 + i)^5/(1 + i*x^6)^6 + x^6*(x^6 + i)^6/(1 + i*x^7)^7 + x^7*(x^7 + i)^7/(1 + i*x^8)^8 + ...
and writing G(x) as a power series in x starting as
G(x) = 1 - x^2 + 2*x^3 + 2*x^4 - 7*x^6 - 2*x^7 + 8*x^8 + 8*x^10 + 12*x^11 - 9*x^12 - 28*x^13 - 16*x^14 + 4*x^15 + 2*x^16 + 46*x^18 + 104*x^19 + 39*x^20 - 100*x^21 - 144*x^22 + 4*x^23 + 16*x^24 - 144*x^25 - 66*x^26 + 28*x^27 + 72*x^28 + 336*x^29 + 533*x^30 + 178*x^31 - 496*x^32 - 448*x^33 + 242*x^34 + 288*x^35 - 298*x^36 - 1032*x^37 - 1212*x^38 - 480*x^39 + 142*x^40 + 1008*x^41 + 2701*x^42 + ...
then the odd coefficients of x^n in G(x), occurring at n = k*(k+1) for k>=0, form this sequence.
PROG
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Feb 10 2019
STATUS
approved