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A123862 Expansion of f(q)*f(q^7)/(f(-q)*f(-q^7)) in powers of q where f() is a Ramanujan theta function. 3
1, 2, 2, 4, 6, 8, 12, 18, 26, 34, 48, 64, 84, 112, 146, 192, 246, 316, 402, 508, 640, 804, 1008, 1248, 1548, 1910, 2344, 2872, 3510, 4276, 5184, 6280, 7578, 9120, 10956, 13128, 15702, 18724, 22292, 26480, 31392, 37148, 43884, 51760, 60912, 71592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A010054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).

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

Euler transform of period 28 sequence [ 2, -1, 2, 0, 2, -1, 4, 0, 2, -1, 2, 0, 2, -2, 2, 0, 2, -1, 2, 0, 4, -1, 2, 0, 2, -1, 2, 0, ...].

G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v)=(u-1)^2 -2*u*v*(v-1).

a(n) ~ exp(2*Pi*sqrt(n/7)) / (4 * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 03 2018

MATHEMATICA

QP := QPochhammer; a[n_]:= SeriesCoefficient[QP[-q]*QP[-q^7]/( QP[q]* QP[q^7]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Jan 04 2018 *)

PROG

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)*eta(x^14+A))^3/ (eta(x+A)*eta(x^7+A))^2/ (eta(x^4+A)*eta(x^28+A)), n))}

CROSSREFS

Cf. A123648(n)=a(n)/2 if n>0.

Sequence in context: A323446 A018129 A091915 * A089647 A274152 A274155

Adjacent sequences:  A123859 A123860 A123861 * A123863 A123864 A123865

KEYWORD

nonn

AUTHOR

Michael Somos, Oct 14 2006

STATUS

approved

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Last modified March 2 05:06 EST 2021. Contains 341741 sequences. (Running on oeis4.)