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A143894 Expansion of (chi(q)^5 * chi(-q))^2 in powers of q where chi() is a Ramanujan theta function. 2
1, 8, 26, 48, 79, 168, 326, 496, 755, 1296, 2106, 3072, 4460, 6840, 10284, 14448, 20165, 29184, 41640, 56880, 77352, 107472, 147902, 197616, 263019, 354888, 475516, 624048, 816065, 1076736, 1413142, 1826416, 2353446, 3050400, 3936754, 5022720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (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

Expansion of q^(1/2) * (eta(q^2)^9 / (eta(q)^4 * eta(q^4)^5))^2 in powers of q.

Euler transform of period 4 sequence [ 8, -10, 8, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (16 t)) = 2 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A143895.

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

a(2*n) = A052241(n). a(2*n + 1) = 8 * A022571(n).

a(n) ~ exp(sqrt(n)*Pi) / (sqrt(2) * n^(3/4)). - Vaclav Kotesovec, Sep 08 2015

EXAMPLE

G.f. = 1 + 8*x + 26*x^2 + 48*x^3 + 79*x^4 + 168*x^5 + 326*x^6 + 496*x^7 + ...

G.f. = 1/q + 8*q + 26*q^3 + 48*q^5 + 79*q^7 + 168*q^9 + 326*q^11 + 496*q^13 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ (QPochhammer[ x^2]^9 / (QPochhammer[ x]^4 QPochhammer[ x^4]^5))^2, {x, 0, n}]; (* Michael Somos, Apr 26 2015 *)

nmax = 40; CoefficientList[Series[Product[((1 + x^k)^4 / (1 + x^(2*k))^5)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 08 2015 *)

PROG

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^9 / (eta(x + A)^4 * eta(x^4 + A)^5))^2, n))};

CROSSREFS

Cf. A022571, A052241, A143895.

Sequence in context: A031307 A122854 A138502 * A126176 A240754 A074238

Adjacent sequences:  A143891 A143892 A143893 * A143895 A143896 A143897

KEYWORD

nonn,changed

AUTHOR

Michael Somos, Sep 04 2008

STATUS

approved

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Last modified November 19 06:26 EST 2019. Contains 329310 sequences. (Running on oeis4.)