The On-Line Encyclopedia of Integer Sequences (OEIS)

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A113277

Expansion of q^(-1/3) * eta(q^2)^5 / eta(q)^2 in powers of q.
(history; published version)

#25 by Alois P. Heinz at Fri Nov 01 19:22:45 EDT 2024

STATUS

proposed

approved

#24 by Michael Somos at Fri Nov 01 18:02:22 EDT 2024

STATUS

editing

proposed

#23 by Michael Somos at Fri Nov 01 18:02:11 EDT 2024

EXAMPLE

G.f. = 1 + 2*x - 4*x^5 - 5*x^8 + 7*x^16 + 8*x^21 - 10*x^33 - 11*x^40 + 13*x^56 + ...

G.f. = q + 2*q^4 - 4*q^16 - 5*q^25 + 7*q^49 + 8*q^64 - 10*q^100 - 11*q^121 +...

PROG

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

(PARI) {a(n) = if(issquare( 3*n + 1, &n), n * (-1)^(n%3 + n), 0)};

(PARI) {a(n) = localmy(A, p, e); if( n<0, 0, n = 3*n + 1; A = factor(n); prod (k=1, matsize(A)[1], if( p=A[k, 1], e=A[k, 2]; if( e%2, 0, (-1)^(p==2) * (-(-1)^(p%3) * p)^(e/2)))))};

STATUS

approved

editing

Discussion

Fri Nov 01

18:02

Michael Somos: Light edits.

#22 by Charles R Greathouse IV at Fri Mar 12 22:24:43 EST 2021

LINKS

M. Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>

Discussion

Fri Mar 12

22:24

OEIS Server: https://oeis.org/edit/global/2897

#21 by N. J. A. Sloane at Wed Nov 13 21:54:13 EST 2019

LINKS

M. Somos, <a href="http://cis.csuohio.edu/~somosA010815/multiqa010815.pdftxt">Introduction to Ramanujan theta functions</a>

Discussion

Wed Nov 13

21:54

OEIS Server: https://oeis.org/edit/global/2830

#20 by Jon E. Schoenfield at Mon Oct 02 03:38:01 EDT 2017

STATUS

editing

approved

#19 by Jon E. Schoenfield at Mon Oct 02 03:37:58 EDT 2017

FORMULA

G.f. is a period 1 Fourier series which satisfies f(-1 / (48 t)) = 3456^(1/2) (t/i)^(3/2) g(t) where q = exp(2 pi Pi i t) and g() is g.f. for A080332.

STATUS

approved

editing

#18 by Bruno Berselli at Tue May 16 11:46:42 EDT 2017

STATUS

proposed

approved

#17 by Seiichi Manyama at Tue May 16 11:20:23 EDT 2017

STATUS

editing

proposed

#16 by Seiichi Manyama at Tue May 16 11:13:49 EDT 2017

LINKS

Seiichi Manyama, <a href="/A113277/b113277.txt">Table of n, a(n) for n = 0..10000</a>

STATUS

approved

editing