id:A136028 - OEIS Search Results

Search: id:A136028

Displaying 1-1 of 1 results found.

page 1

Expansion of (phi(q) * phi(q^2))^3 in powers of q where phi() is a Ramanujan theta function.

+0
1

1, 6, 18, 44, 90, 144, 212, 288, 330, 418, 528, 588, 836, 1008, 1056, 1440, 1386, 1356, 1894, 1644, 2064, 2880, 2484, 3168, 3428, 2838, 3696, 3864, 4128, 5040, 5280, 5760, 5418, 5656, 5988, 5376, 7678, 8208, 7572, 10080, 8208, 7788, 10560, 8652, 10404 (list; graph; listen)

	OFFSET	`0,2`
	FORMULA	`Expansion of (eta(q^2) * eta(q^4))^9 / (eta(q) * eta(q^8))^6 in powers of q.` `G.f. is Fourier series of a weight 3 level 8 modular form. f(-1/(8 t)) = 2^(9/2) (t/i)^3 f(t) where q = exp(2 pi i t).` `G.f.: (Product_{k>0} (1 - x^k)^2 * (1 + x^k)^4 * (1 + x^(2k)) / (1 + x^(4k))^2)^3.`
	EXAMPLE	`1 + 6q + 18q^2 + 44q^3 + 90q^4 + 144q^5 + 212q^6 + 288*q^7 + ...`
	PROGRAM	`(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( ((eta(x^2 + A) * eta(x^4 + A))^3 / (eta(x + A) * eta(x^8 + A))^2)^3, n))}`
	CROSSREFS	`Convolution of A033715 and A097057. a(n) = A029713(n) + 6 * A030207(n).` `Sequence in context: A009957 A011929 A070735 this_sequence A083719 A095170 A128543` `Adjacent sequences: A136025 A136026 A136027 this_sequence A136029 A136030 A136031`
	KEYWORD	`nonn`
	AUTHOR	`Michael Somos, Dec 10 2007`

page 1

Search completed in 0.002 seconds

Last modified March 20 09:10 EDT 2010. Contains 173642 sequences.

AT&T Labs Research