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Search: id:A035036
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| A035036 |
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Fourier coefficients of E_{gamma,2}*E_{0,4}. |
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+0
1
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| 1, 8, -248, 1952, -8440, 25008, -60512, 134464, -270584, 474344, -775248, 1288416, -2059360, 2970352, -4168384, 6101952, -8659192, 11358864, -14704664, 19808800, -26383440, 32809216, -39940896, 51490752, -66022496, 78150008, -92080912, 115265600, -141859520
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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E_{gamma,2}*E_{0,4} is the unique normalized weight-6 modular form for \Gamma_0(2) with an order 1/2 zero at \gamma = -1/2+i/2 and an order 1 zero at 0.
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LINKS
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B. Brent, Quadratic Minima and Modular Forms, Experimental Mathematics, v.7 no.3, 257-274.
H. H. Chan and C. Krattenthaler, Recent progress in the study of representations of integers as sums of squares
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FORMULA
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G.f.: 1 - 8 * Sum[k=1..inf, k^5*q^k/(1-(-q)^k)].
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EXAMPLE
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E_{gamma,2}*E_{0,4}=1+8q-248q^2+...
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PROGRAM
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(PARI) a(n)=if(n<1, n==0, 8*(sigma(n, 5)-if(n%2, 0, 64*sigma(n/2, 5)))) /* Michael Somos, Jul 16 2004 */
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CROSSREFS
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Adjacent sequences: A035033 A035034 A035035 this_sequence A035037 A035038 A035039
Sequence in context: A053089 A090241 A029751 this_sequence A138323 A053717 A034674
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KEYWORD
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easy,sign
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AUTHOR
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Barry Brent (barryb(AT)primenet.com)
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