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 A161361 #28 Mar 06 2018 11:38:46
%S A161361 1,372,29250,-134120,54261375,-6139293372,854279148734,
%T A161361 -128813964933000,20657907916144515,-3469030105750871000,
%U A161361 603760629237519966018,-108124880417607682194048,19820541224206810447813500
%N A161361 Convolution square root of A000521.
%C A161361 Triangle A161362 = the corresponding convolution triangle with row sums = A000521.
%H A161361 Seiichi Manyama, <a href="/A161361/b161361.txt">Table of n, a(n) for n = 0..426</a>
%F A161361 Given A000521: (j = 1/q + 744 + 196884q + 21493760q^2 + 864299970q^3 + ...); multiply by q and take the convolution square root.
%F A161361 G.f. is a period 1 Fourier series which satisfies f(-1 / (4 t)) = f(t) where q = exp(2 Pi i t). - _Michael Somos_, May 03 2014
%F A161361 G.f.: Product_{n>=1} (1-q^n)^(A192731(n)/2). - _Seiichi Manyama_, Jul 02 2017
%F A161361 a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(5/2), where c = 0.378271951998085144930610869223050101960774818... = 3^(5/2) * Gamma(1/3)^9 / (2^(7/2) * exp(sqrt(3) * Pi/2) * Pi^(13/2)). - _Vaclav Kotesovec_, Jul 03 2017, updated Mar 06 2018
%F A161361 a(n) * A299832(n) ~ 3*exp(2*sqrt(3)*Pi*n) / (2*Pi*n^2). - _Vaclav Kotesovec_, Feb 20 2018
%e A161361 a(2) = 29250 = 1/2 * (A000521(2) - 372^2) = 1/2 * (196884 - 138384) = 29250.
%e A161361 G.f. = 1 + 372*x + 29250*x^2 - 134120*x^3 + 54261375*x^4 - ...
%e A161361 G.f. = 1/q + 372*q + 29250*q^3 - 134120*q^5 + 54261375*q^7 + ...
%t A161361 CoefficientList[Series[(65536 + x*QPochhammer[-1, x]^24)^(3/2) / (4096 * QPochhammer[-1, x]^12), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Sep 23 2017 *)
%o A161361 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); A = x * (eta(x^2 + A) / eta(x + A))^24; polcoeff( sqrt(x * (1 + 256*A)^3 / A), n))}; /* _Michael Somos_, May 03 2014 */
%Y A161361 Cf. A000521, A161362, A192731.
%Y A161361 (q*j(q))^(k/24): A289397 (k=-1), A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), A289300 (k=5), A289301 (k=6), A289302 (k=7), A007245 (k=8), A289303 (k=9), A289304(k=10), A289305 (k=11), this sequence (k=12).
%K A161361 sign
%O A161361 0,2
%A A161361 _Gary W. Adamson_, Jun 07 2009
%E A161361 More terms from _R. J. Mathar_, Jun 15 2009
%E A161361 Keyword:sign introduced by _R. J. Mathar_, Jul 07 2009