A285638 G.f.: (1 - x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - ...))))) * (1 + x/(1 + x^2/(1 + x^3/(1 + x^4/(1 + ...))))), a continued fraction.

1, 0, -1, -2, 0, 0, -1, -4, -4, -2, -3, -6, -13, -16, -19, -24, -38, -60, -82, -110, -150, -224, -324, -458, -637, -898, -1289, -1838, -2609, -3680, -5223, -7430, -10571, -15004, -21272, -30202, -42903, -60960, -86543, -122860, -174450, -247762, -351883, -499668, -709521, -1007532

Offset

0,4

Links

Table of n, a(n) for n=0..45.

Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

Formula

G.f.: A(x) = Q(x)/(R(x)*P(x)), where Q(x) = Sum_{k>=0} (-1)^k*x^(k^2) / Product_{m=1..k} (1 - x^m), R(x) = Product_{k>=1} (1 - x^(5*k-1))*(1 - x^(5*k-4)) / ((1 - x^(5*k-2))*(1 - x^(5*k-3)) and P(x) = Sum_{k>=0} (-1)^k*x^(k*(k+1)) / Product_{m=1..k} (1 - x^m).

Example

G.f.: A(x) = 1 - x^2 - 2*x^3 - x^6 - 4*x^7 - 4*x^8 - 2*x^9 - 3*x^10 - 6*x^11 - 13*x^12 - ...

Mathematica

nmax = 45; CoefficientList[Series[1/((1/(1 + ContinuedFractionK[-x^k, 1, {k, 1, nmax}])) (1/(1 + ContinuedFractionK[x^k, 1, {k, 1, nmax}]))), {x, 0, nmax}], x]
nmax = 45; CoefficientList[Series[Sum[(-1)^k x^(k^2)/Product[(1 - x^m), {m, 1, k}], {k, 0, nmax}] / (Sum[(-1)^k x^(k (k + 1))/Product[(1 - x^m), {m, 1, k}], {k, 0,
nmax}] Product[(1 - x^(5 k - 1)) (1 - x^(5 k - 4))/((1 - x^(5 k - 2)) (1 - x^(5 k - 3))), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A003823, A005169, A007325, A055101, A285635, A285636, A285637.

Sequence in context: A256282 A258256 A361290 * A325667 A067310 A369321

Adjacent sequences: A285635 A285636 A285637 * A285639 A285640 A285641

Keyword

sign

Author

Ilya Gutkovskiy, Apr 23 2017

Status

approved