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Search: id:A053253
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| A053253 |
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Coefficients of the '3rd order' mock theta function omega(q) |
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+0
9
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| 1, 2, 3, 4, 6, 8, 10, 14, 18, 22, 29, 36, 44, 56, 68, 82, 101, 122, 146, 176, 210, 248, 296, 350, 410, 484, 566, 660, 772, 896, 1038, 1204, 1391, 1602, 1846, 2120, 2428, 2784, 3182, 3628, 4138, 4708, 5347, 6072, 6880, 7784, 8804, 9940, 11208, 12630
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Leila A. Dragonette, Some asymptotic formulae for the mock theta functions of Ramanujan, Trans. Amer. Math. Soc., 72 (1952) 474-500
Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 15, 17, 31
George N. Watson, The final problem: an account of the mock theta functions, J. London Math. Soc., 11 (1936) 55-80
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FORMULA
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G.f.: omega(q) = sum for n >= 0 of q^(2n(n+1))/((1-q)(1-q^3)...(1-q^(2n+1)))^2
G.f.: Sum_{k>=0} x^k/((1-x)(1-x^3)...(1-x^(2k+1))). - Michael Somos Aug 18 2006
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MATHEMATICA
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Series[Sum[q^(2n(n+1))/Product[1-q^(2k+1), {k, 0, n}]^2, {n, 0, 6}], {q, 0, 100}]
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=1+x*O(x^n); polcoeff( sum(k=0, (sqrtint(2*n+1)-1)\2, A*=(x^(4*k)/(1-x^(2*k+1))^2 +x*O(x^(n-2*(k^2-k))))), n))} /* Michael Somos Aug 18 2006 */
(PARI) {a(n)=local(A); if(n<0, 0, n++; A=1+x*O(x^n); polcoeff( sum(k=0, n-1, A*=(x/(1-x^(2*k+1)) +x*O(x^(n-k)))), n))} /* Michael Somos Aug 18 2006 */
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CROSSREFS
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Other '3rd order' mock theta functions are at A000025, A053250, A053251, A053252, A053254, A053255.
Cf. A095913(n)=a(n-3).
Sequence in context: A003107 A014977 A008583 this_sequence A095913 A102848 A134157
Adjacent sequences: A053250 A053251 A053252 this_sequence A053254 A053255 A053256
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KEYWORD
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nonn,easy
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AUTHOR
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Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 19 1999
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