A064053 -id:A064053 - cp's OEIS frontend

A085142 Duplicate of A064053.

1, 0, -4, 4, -4, 4, -4, 8, -4, 0, -4, 8, -4, 0, -4, 4, -4, 0, 0, 8, -4, -4, -4, 8, 0, 0, 0, 4, -4, 0, -4, 8, -4, -4, 0

Offset: 0

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A096661 Fine's numbers J(n).

0, 0, -1, 1, -1, 1, -1, 2, -1, 0, -1, 2, -1, 0, -1, 1, -1, 0, 0, 2, -1, -1, -1, 2, 0, 0, 0, 1, -1, 0, -1, 2, -1, -1, 0, 2, 0, 0, -2, 1, -2, 0, 1, 2, -1, 0, -2, 2, 0, 0, -1, 1, -1, 0, -1, 3, -1, 0, 0, 2, -1, 0, -2, 0, -1, 1, 1, 2, -1, 0, -3, 2, 0, 0, 0, 1, -1, -1, -1, 2, -2, 0, 0, 2, 1, 1, -2, 0, -1, 0, 0, 1, -1, 0, -2, 3, 0, 0, 1, 0, -1, 0, -1, 2, -1

Offset: 0

N. J. A. Sloane, Sep 15 2004

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			G.f. = - x^2 + x^3 - x^4 + x^5 - x^6 + 2*x^7 - x^8 - x^10 + 2*x^11 - x^12 + ...

N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 62, Eq. (27.1).

G. C. Greubel, Table of n, a(n) for n = 0..5000
L. A. Dragonette, Some Asymptotic Formulae for the Mock Theta Series of Ramanujan, Trans. Amer. Math. Soc., 72 (1952), 474-500. See page 496.

Cf. A064053, A097042.

add( (-1)^n*q^((3*n^2+n)/2)/(1+q^n),n=1..10);

a[n_]:= SeriesCoefficient[Sum[(-1)^k*q^((3*k^2 + k)/2)/(1 + q^k), {k, 1, 2*nmax}], {q,0,n}]; Table[a[n], {n,0,50}] (* G. C. Greubel, Feb 18 2018 *)

{a(n) = if( n<0, 0, polcoeff( sum(k=1, (sqrtint(24*n + 1) - 1) \ 6, (-1)^k * x^((3*k^2 + k)/2) / (1 + x^k), x * O(x^n)), n))}; /* Michael Somos, Mar 13 2006 */

G.f.: Sum_{n >= 1} (-1)^n*q^((3*n^2+n)/2)/(1+q^n).

Dragonette's gamma(n) = A064053(n) = 4*a(n) if n>0.

A109471 Cumulative sum of absolute values of coefficients of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).

Original entry on oeis.org

1, 3, 6, 11, 17, 27, 38, 55, 76, 103, 136, 182, 235, 303, 385, 489, 612, 766, 945, 1166, 1428, 1742, 2111, 2557, 3072, 3686, 4401, 5246, 6223, 7371, 8692, 10236, 12014, 14074, 16435, 19171, 22292, 25884, 29981, 34677, 40017, 46122, 53038, 60920

Offset: 0

Jonathan Vos Post, Aug 28 2005

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Cf. A000039, A000019, A053250, A053251, A053252, A053253, A053254, A053255, A064053.

nmax = 200; f[q_, s_] := Sum[q^(n^2)/Product[1 + q^k, {k, n}]^2, {n, 0, s}]; A000039:= CoefficientList[Series[f[q, nmax], {q, 0, nmax}], q][[1 ;; -1 ;; 2]]; Table[Sum[Abs[A000039[[k]]], {k,1,n}], {n,1,51}] (* G. C. Greubel, Feb 18 2018 *)

a(n) = Sum_{k=0..n} abs(A000039(k)). [corrected by Joerg Arndt, Feb 25 2018]

a(n) ~ sqrt(3/2) * exp(sqrt(n/3)*Pi) / Pi. - Vaclav Kotesovec, Jun 12 2019

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A085142 Duplicate of A064053.

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A096661 Fine's numbers J(n).

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A109471 Cumulative sum of absolute values of coefficients of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).

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