id:A145740 - OEIS Search Results

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McKay-Thompson series of class 20C for the Monster group with a(0) = -2.

+0
2

1, -2, 1, -2, 2, 2, -1, 0, -4, 2, 5, -2, 0, -8, 2, 8, -3, 2, -14, 6, 14, -6, 4, -24, 12, 24, -11, 4, -40, 16, 38, -16, 5, -62, 24, 60, -24, 10, -94, 40, 91, -38, 18, -144, 62, 136, -57, 24, -214, 88, 201, -82, 30, -308, 122, 288, -117, 48, -440, 180, 410, -168, 74, -624, 262, 578, -238, 96, -874, 356, 804 (list; graph; listen)

	OFFSET	`-1,2`
	FORMULA	`Expansion of (eta(q) * eta(q^4) * eta(q^10) / (eta(q^2) * eta(q^5) * eta(q^20)))^2 in powers of q.` `G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = 5 / f(t) where q = exp(2 pi i t).` `Expansion of q^(-1) * (psi(-q) / psi(-q^5))^2 in powers of q where psi() is a Ramanujan theta function.`
	EXAMPLE	`1/q - 2 + q - 2q^2 + 2q^3 + 2q^4 - q^5 - 4q^7 + 2q^8 + 5q^9 + ...`
	PROGRAM	`(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^4 + A) * eta(x^10 + A) / (eta(x^2 + A) * eta(x^5 + A) * eta(x^20 + A)))^2, n))}`
	CROSSREFS	`A112159(n) = a(n) unless n=0. Convolution square of A145708. -2 * A138522(n) = a(2*n).` `Sequence in context: A134997 A104605 A138516 this_sequence A026513 A106028 A105307` `Adjacent sequences: A145737 A145738 A145739 this_sequence A145741 A145742 A145743`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Oct 17 2008`

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Last modified December 20 16:54 EST 2009. Contains 171081 sequences.

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