A294065 Row 2 in rectangular array A292929.

2, -4, 8, -14, 18, -36, 56, -74, 116, -164, 224, -324, 442, -592, 808, -1074, 1410, -1860, 2416, -3102, 4010, -5112, 6464, -8204, 10294, -12860, 16072, -19914, 24586, -30356, 37248, -45534, 55608, -67604, 81928, -99182, 119608, -143832, 172760, -206834, 247048, -294676, 350504, -416080, 493248, -583340, 688616, -811740, 954974, -1121564, 1315504, -1540210, 1800434, -2102060, 2450224, -2852040

Offset

0,1

Links

Paul D. Hanna, Table of n, a(n) for n = 0..380

Example

G.f.: A(q) = 2 - 4*q + 8*q^2 - 14*q^3 + 18*q^4 - 36*q^5 + 56*q^6 - 74*q^7 + 116*q^8 - 164*q^9 + 224*q^10 - 324*q^11 + 442*q^12 - 592*q^13 + 808*q^14 - 1074*q^15 + 1410*q^16 - 1860*q^17 + 2416*q^18 - 3102*q^19 + 4010*q^20 +...
RELATED SERIES.
Let R1(q) denote the g.f. of row 1 (with offset 0) in array A292929, then
A(q)/R1(q) = 1 + q^2 + q^3 - 3*q^5 + q^6 + 4*q^7 + q^8 - 3*q^9 + q^10 + 3*q^11 + q^12 - 5*q^13 + q^14 + 7*q^15 - 11*q^17 + 16*q^19 + 2*q^20 - 18*q^21 + 21*q^23 + q^24 - 27*q^25 + q^26 + 38*q^27 + q^28 - 55*q^29 + 2*q^30 +...
then it appears that the even bisection of A(q)/R1(q) forms a g.f. of A053692:
(A(q)/R1(q) + A(-q)/R1(-q))/2 = Product_{n>=1} (1 - q^(16*n))^2*(1 + q^(4*n-2)).

Mathematica

nmax = 55; kmax = Ceiling[Sqrt[nmax]];
Q[q_] := Sum[(x - q^k)^k, {k, -kmax, kmax}];
S[q_] := Sqrt[Q[q]/Q[-q]];
row[n_] := (1/q^n)*SeriesCoefficient[Sqrt[Q[q]/Q[-q]], {x, 0, n}] + O[q]^nmax // CoefficientList[#, q]&;
row[2] (* Jean-François Alcover, Nov 04 2017 *)

Crossrefs

Cf. A292929, A293132, A294066, A294067.

Sequence in context: A084621 A248379 A002132 * A248845 A370047 A169926

Adjacent sequences: A294062 A294063 A294064 * A294066 A294067 A294068

Keyword

sign

Author

Paul D. Hanna, Oct 23 2017

Status

approved