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A281492 Expansion of f(x, x^3) * f(x^4, x^5) in powers of x where f(, ) is Ramanujan's general theta function. 4
1, 1, 0, 1, 1, 2, 2, 1, 1, 0, 2, 1, 0, 0, 1, 2, 0, 1, 1, 2, 3, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1, 1, 3, 1, 2, 1, 0, 4, 0, 1, 1, 2, 1, 0, 1, 1, 1, 2, 0, 1, 0, 1, 2, 0, 1, 1, 1, 0, 1, 1, 0, 0, 3, 2, 1, 1, 2, 2, 1, 1, 2, 0, 2, 0, 1, 2, 2, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

f(a,b) = 1 + Sum_{k=1..oo} (ab)^(k(k-1)/2)*(a^k+b^k). - N. J. A. Sloane, Jan 30 2017

Euler transform of period 18 sequence [1, -1, 1, 0, 2, -1, 1, -2, 0, -2, 1, -1, 2, 0, 1, -1, 1, -2, ...].

G.f.: (Sum_{k>0} x^(k*(k - 1)/2)) * (Sum_{k in Z} x^(k*(9*k + 1)/2)).

G.f.: Product_{k>0} (1 - x^(2*k)) / (1 - x^(2*k-1)) * (1 + x^(9*k-5)) * (1 + x^(9*k-4)) * (1 - x^(9*k)).

2 * a(n) = A281451(128*n + 17).

EXAMPLE

G.f. = 1 + x + x^3 + x^4 + 2*x^5 + 2*x^6 + x^7 + x^8 + 2*x^10 + x^11 + ...

G.f. = q^5 + q^41 + q^113 + q^149 + 2*q^185 + 2*q^221 + q^257 + q^293 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ (1/2) x^(-1/8) EllipticTheta[ 2, 0, x^(1/2)] QPochhammer[ -x^4, x^9] QPochhammer[ -x^5, x^9] QPochhammer[ x^9], {x, 0, n}];

PROG

(PARI) {a(n) = if( n<0, 0, sumdiv(36*n + 5, d, kronecker(-4, d)) / 2)};

CROSSREFS

Cf. A281451.

Sequence in context: A185304 A081389 A133685 * A112183 A275451 A269317

Adjacent sequences:  A281489 A281490 A281491 * A281493 A281494 A281495

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 29 2017

STATUS

approved

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Last modified September 28 01:20 EDT 2020. Contains 337388 sequences. (Running on oeis4.)