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A281491 Expansion of f(x, x^3) * f(x^2, x^7) in powers of x where f(, ) is Ramanujan's general theta function. 4
1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 1, 2, 0, 1, 0, 1, 1, 3, 1, 0, 1, 0, 3, 1, 1, 0, 0, 2, 2, 1, 2, 0, 2, 1, 0, 1, 0, 2, 1, 1, 0, 1, 2, 2, 0, 2, 1, 0, 2, 1, 0, 1, 2, 1, 0, 1, 2, 2, 0, 1, 1, 0, 4, 2, 0, 0, 1, 1, 0, 0, 1, 1, 3, 1, 1, 0, 1, 2, 1, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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

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

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

G.f.: Product_{k>0} (1 - x^(2*k)) / (1 - x^(2*k-1)) * (1 + x^(9*k-7)) * (1 + x^(9*k-2)) * (1 - x^(9*k)).

2 * a(n) = A281451(8*n + 3).

EXAMPLE

G.f. = 1 + x + x^2 + 2*x^3 + x^5 + x^6 + x^7 + 2*x^8 + 2*x^10 + x^12 + ...

G.f. = q^17 + q^53 + q^89 + 2*q^125 + q^197 + q^233 + q^269 + 2*q^305 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ (1/2) x^(-1/8) EllipticTheta[ 2, 0, x^(1/2)] QPochhammer[ -x^2, x^9] QPochhammer[ -x^7, x^9] QPochhammer[ x^9], {x, 0, n}];

PROG

(PARI) {a(n) = if( n<0, 0, sumdiv(36*n + 17, d, kronecker(-4, d)) / 2)};

CROSSREFS

Cf. A281451.

Sequence in context: A286934 A282714 A280634 * A099494 A030341 A258832

Adjacent sequences:  A281488 A281489 A281490 * A281492 A281493 A281494

KEYWORD

nonn

AUTHOR

Michael Somos, Jan 29 2017

STATUS

approved

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Last modified November 23 16:18 EST 2020. Contains 338590 sequences. (Running on oeis4.)