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 A261526 #21 Feb 16 2025 08:33:26
%S A261526 1,2,5,8,14,22,36,54,83,120,176,250,356,494,687,936,1276,1714,2298,
%T A261526 3046,4030,5280,6902,8952,11580,14882,19077,24314,30910,39104,49344,
%U A261526 62000,77712,97032,120872,150058,185869,229520,282814,347504,426118,521182,636204
%N A261526 Expansion of (H(-x) / chi(-x))^2 in powers of x where chi() is a Ramanujan theta function and G() is a Rogers-Ramanujan function.
%C A261526 Rogers-Ramanujan functions: G(q) (see A003114), H(q) (A003106).
%C A261526 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A261526 G. C. Greubel, <a href="/A261526/b261526.txt">Table of n, a(n) for n = 0..2500</a>
%H A261526 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A261526 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A261526 Euler transform of period 20 sequence [ 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, ...].
%F A261526 Expansion of (f(x, -x^4) / f(-x^2, -x^2))^2 = (f(x^2, x^8) / f(-x, -x^4))^2 in powers of x where f(, ) is Ramanujan's general theta function.
%F A261526 G.f.: (Sum_{k>=0} x^(k^2 + k) / ((1 - x) * (1 - x^2) * ... * (1 - x^(2*k+1))))^2.
%F A261526 a(n) = - A147699(5*n + 2).
%F A261526 Convolution square of A122135.
%e A261526 G.f. = 1 + 2*x + 5*x^2 + 8*x^3 + 14*x^4 + 22*x^5 + 36*x^6 + 54*x^7 + ...
%e A261526 G.f. = q^9 + 2*q^29 + 5*q^49 + 8*q^69 + 14*q^89 + 22*q^109 + 36*q^129 + ...
%t A261526 a[ n_] := SeriesCoefficient[ (QPochhammer[ x, x^2] QPochhammer[ x^2, -x^5] QPochhammer[ -x^3, -x^5])^-2, {x, 0, n}];
%t A261526 a[ n_] := SeriesCoefficient[ Product[ (1 - x^k)^-{2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0}[[Mod[k, 20, 1]]], {k, n}], {x, 0, n}];
%o A261526 (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x * O(x^n))^-[ 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2][k%20 + 1]), n))};
%o A261526 (PARI) {a(n) = if( n<0, 0, polcoeff( sum(k=0, (sqrtint(4*n + 1) - 1)\2, x^(k^2 + k)/ prod(i=1, 2*k+1, 1 - x^i, 1 + x * O(x^(n - k^2-k))))^2, n))};
%Y A261526 Cf. A122135, A147699.
%K A261526 nonn
%O A261526 0,2
%A A261526 _Michael Somos_, Sep 03 2015