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A258939 Expansion of f(-x^3, -x^5) * f(x^3, x^13) / (f(-x, -x^2) * f(-x^8, -x^16)) in powers of x where f(, ) is Ramanujan's general theta function. 2
1, 1, 2, 3, 5, 6, 9, 12, 17, 22, 30, 38, 51, 64, 83, 104, 133, 165, 208, 256, 319, 390, 481, 584, 715, 863, 1047, 1258, 1517, 1812, 2172, 2584, 3080, 3648, 4327, 5104, 6028, 7084, 8330, 9756, 11430, 13340, 15574, 18122, 21086, 24464, 28378, 32832, 37977, 43823 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

LINKS

Table of n, a(n) for n=0..49.

M. Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

FORMULA

Euler transform of period 32 sequence [ 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, ...].

- a(n) = A029838(4*n + 2).

a(n) ~ sqrt(2*(1+sqrt(2))) * exp(Pi*sqrt(n/2)) / (16*n^(3/4)). - Vaclav Kotesovec, Nov 07 2015

EXAMPLE

G.f. = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 6*x^5 + 9*x^6 + 12*x^7 + 17*x^8 + ...

G.f. = q^15 + q^47 + 2*q^79 + 3*q^111 + 5*q^143 + 6*q^175 + 9*q^207 + ...

MATHEMATICA

a[ n_] := SeriesCoefficient[ Product[ (1 - x^k)^-{ 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0}[[Mod[k, 32, 1]]], {k, n}], {x, 0, n}];

PROG

(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^-[ 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1][k%32 + 1]), n))};

CROSSREFS

Cf. A029838.

Sequence in context: A225973 A292444 A035948 * A244747 A241742 A212584

Adjacent sequences:  A258936 A258937 A258938 * A258940 A258941 A258942

KEYWORD

nonn

AUTHOR

Michael Somos, Nov 07 2015

STATUS

approved

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Last modified June 26 20:24 EDT 2019. Contains 324380 sequences. (Running on oeis4.)