A323691 Odd coefficients in Sum_{n>=0} (x^(n+1) + i)^n / (1 + i*x^n)^(n+1), in which the constant term is taken to be 1.

1, 1, 11, 35, 95, 73, -6809, -37129, -49763, -118151, 3098985, 18490177, 135754015, 476263867, -1506027797, -77594009, -9795145237, -181840242713, -1625887512417, -14848078415067, -80493076445459, -304934409547939, -440055933017985, -4208587849042603, -23584916465354149, 249312361064897267, 2617671685008217267, 17522498092619009285, 100559736578029630325, 519821481713769303651, 1604365446162860783027

Offset

0,3

Comments

a(n) = A323690(n*(n+1)).

Links

Paul D. Hanna, Table of n, a(n) for n = 0..100

Example

The generating function of A323690 is
G(x) = Sum_{n>=0} (x^(n+1) + i)^n / (1 + i*x^n)^(n+1),
in which the constant term is taken to be 1, so that
G(x) = 1 + 2*x + x^2 - 8*x^3 + 18*x^5 + 11*x^6 - 16*x^7 - 44*x^8 + 36*x^10 - 12*x^11 + 35*x^12 + 112*x^13 + 56*x^14 - 144*x^15 - 260*x^16 - 88*x^17 + 48*x^18 - 20*x^19 + 95*x^20 + 504*x^21 + 636*x^22 + 288*x^23 - 578*x^24 - 1016*x^25 - 292*x^26 - 216*x^27 - 624*x^28 - 210*x^29 + 73*x^30 + ...
This sequence gives the odd coefficients of x^n, which occur at n = k*(k+1) for k >= 0.

Prog

(PARI) {A323690(n) = my(SUM = sum(m=0, n, (x^(m+1) + I +x*O(x^n))^m / (1 + I*x^m +x*O(x^n))^(m+1) ) ); polcoeff(1 + SUM - I^n/(1+I), n)}
{a(n) = A323690(n*(n+1))}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A323690.

Sequence in context: A003777 A222512 A297539 * A368743 A199817 A216034

Adjacent sequences: A323688 A323689 A323690 * A323692 A323693 A323694

Keyword

sign

Author

Paul D. Hanna, Feb 13 2019

Status

approved