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Search: id:A143184
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| A143184 |
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Coefficients of a Ramanujan q-series. |
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+0
1
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| 1, 1, 2, 4, 6, 10, 15, 23, 33, 49, 69, 98, 136, 188, 256, 348, 466, 622, 824, 1084, 1418, 1846, 2389, 3077, 3947, 5038, 6407, 8115, 10241, 12876, 16141, 20160, 25110, 31179, 38609, 47674, 58724, 72141, 88421, 108114, 131902, 160565, 195061, 236468
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 10
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FORMULA
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G.f.: Sum_{k>=0} x^((k^2+k)/2) / ((1 - x) * (1 - x^2) ... (1 - x^k))^2
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EXAMPLE
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1 + q + 2*q^2 + 4*q^3 + 6*q^4 + 10*q^5 + 15*q^6 + 23*q^7 + 33*q^8 + ...
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PROGRAM
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(PARI) {a(n)= local(t); if( n<0, 0, t = 1 +x*O(x^n); polcoeff( sum(k=1, (sqrtint(8*n+1)-1)\2, t = t* x^k/ (1-x^k)^2 +x*O(x^n), 1), n))}
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CROSSREFS
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Convolution with A002448 is A132211.
Sequence in context: A086182 A035294 A073818 this_sequence A116084 A108925 A120549
Adjacent sequences: A143181 A143182 A143183 this_sequence A143185 A143186 A143187
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jul 28 2008
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