This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A064053 #43 Feb 16 2025 08:32:45
%S 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,
%T A064053 -4,0,-4,8,-4,-4,0,8,0,0,-8,4,-8,0,4,8,-4,0,-8,8,0,0,-4,4,-4,0,-4,12,
%U A064053 -4,0,0,8,-4,0,-8,0,-4,4,4,8,-4,0,-12,8,0,0,0,4,-4,-4,-4,8,-8,0,0,8,4,4,-8,0,-4,0,0,4,-4,0,-8,12,0,0,4,0,-4,0,-4
%N A064053 Auxiliary sequence gamma(n) used to compute coefficients in series expansion of the mock theta function f(q) via A(n) = Sum_{r=0..n} p(r)*gamma(n-r), with p(r) the partition function A000041.
%C A064053 See Dragonette for the definition of f(q) and A(n). - _N. J. A. Sloane_, Sep 24 2022
%D A064053 G. E. Andrews, The theory of partitions, Cambridge University Press, Cambridge, 1998, page 82, Example 5. MR1634067 (99c:11126). [The Gamma function used by Andrews is the classical Gamma function, which is different from the gamma(n) of this sequence. - _N. J. A. Sloane_, Sep 24 2022]
%H A064053 G. C. Greubel, <a href="/A064053/b064053.txt">Table of n, a(n) for n = 0..5000</a>
%H A064053 L. A. Dragonette, <a href="http://dx.doi.org/10.1090/S0002-9947-1952-0049927-8">Some Asymptotic Formulae for the Mock Theta Series of Ramanujan</a>, Trans. Amer. Math. Soc., 72 (1952), 474-500. See page 496.
%H A064053 L. A. Dragonette, <a href="/A064053/a064053.png">Some Asymptotic Formulae for the Mock Theta Series of Ramanujan</a>, Trans. Amer. Math. Soc., 72 (1952), 474-500. Enlargement of a portion of page 496 in order to show correct spelling of gamma(n).
%H A064053 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MockThetaFunction.html">Mock Theta Function.</a>
%F A064053 G.f.: 1 + 4 * Sum_{k>0} (-1)^k * x^(k*(3*k + 1)/2) / (1 + x^k). - _Michael Somos_, Jun 19 2003
%F A064053 Convolution of this sequence and A000041 is A000025. - _Michael Somos_, Jun 19 2003
%F A064053 a(n) = 4 * A096661(n) unless n=0.
%e A064053 G.f. = 1 - 4*x^2 + 4*x^3 - 4*x^4 + 4*x^5 - 4*x^6 + 8*x^7 - 4*x^8 - 4*x^10 + 8*x^11 - 4*x^12 - ...
%t A064053 a[ n_]:= SeriesCoefficient[1 +4 *Sum[(-1)^k*x^(k*(3*k+1)/2)/(1+x^k), {k, Quotient[Sqrt[1 +24*n] - 1, 6]}], {x, 0, n}]; (* _Michael Somos_, Apr 08 2015 *)
%o A064053 (PARI) {a(n) = if( n<1, n==0, 4 * 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 */
%Y A064053 Cf. A000025, A000039, A000041, A000199, A096661.
%K A064053 sign
%O A064053 0,3
%A A064053 _Eric W. Weisstein_, Aug 28 2001
%E A064053 Entry revised by _Michael Somos_, Mar 13 2006
%E A064053 Deleted edit that tried to change gamma(n) to Gamma(n), and restored original definition. - _N. J. A. Sloane_, Sep 24 2022