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A134340 Expansion of psi(x)^3 * f(-x^3)^3 / chi(-x)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions. 3
1, 5, 12, 22, 35, 50, 70, 92, 117, 145, 170, 210, 250, 287, 330, 362, 425, 477, 532, 600, 626, 715, 782, 850, 925, 962, 1100, 1162, 1247, 1335, 1370, 1520, 1617, 1750, 1810, 1850, 2040, 2147, 2262, 2380, 2451, 2625, 2752, 2882, 3015, 3005, 3290, 3500, 3577 (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..10000

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Expansion of q^(-5/6) * eta(q^2)^8 * eta(q^3)^3 / eta(q)^5 in powers of q.

Euler transform of period 6 sequence [ 5, -3, 2, -3, 5, -6, ...].

-24 * a(n) = A103440(6*n + 5). 216 * a(n) = A109041(6*n + 5).

EXAMPLE

G.f. = 1 + 5*x + 12*x^2 + 22*x^3 + 35*x^4 + 50*x^5 + 70*x^6 + 92*x^7 + 117*x^8 + ...

G.f. = q^5 + 5*q^11 + 12*q^17 + 22*q^23 + 35*q^29 + 50*q^35 + 70*q^41 + 94*q^47 + ...

MATHEMATICA

a[ n_] := If[ n < 0, 0, (-1/24) DivisorSum[ 6 n + 5, #^2 KroneckerSymbol[ -3, #] &]]; (* Michael Somos, Oct 25 2015 *)

a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x]^2 QPochhammer[ x^3]^3 EllipticTheta[ 2, 0, x^(1/2)]^3 / (8 x^(3/8)), {x, 0, n}]; (* Michael Somos, Oct 25 2015 *)

PROG

(PARI) {a(n) = if( n<0, 0, n = 6*n + 5; sumdiv(n, d, d^2 * kronecker( -3, d)) / -24 )};

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^8 * eta(x^3 + A)^3 / eta(x + A)^5, n))};

CROSSREFS

Cf. A103440, A109041.

Sequence in context: A131976 A074376 A293502 * A000326 A022795 A025734

Adjacent sequences:  A134337 A134338 A134339 * A134341 A134342 A134343

KEYWORD

nonn

AUTHOR

Michael Somos, Oct 21 2007

STATUS

approved

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Last modified December 13 18:19 EST 2018. Contains 318086 sequences. (Running on oeis4.)