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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A199817 A216034 A224790

Adjacent sequences:  A323688 A323689 A323690 * A323692 A323693 A323694

KEYWORD

sign

AUTHOR

Paul D. Hanna, Feb 13 2019

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)