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 A278194 #10 May 05 2020 01:59:30
%S A278194 0,0,1,-14,336,-1408,256256,14746368,1766772736,242121048064,
%T A278194 41267065061376,8461792420167680,2057680174397259776,
%U A278194 585429994601202057216,192659868531986620481536,72616356304572571212316672,31078397531081274526066016256
%N A278194 E.g.f. (1/5!)*sin^5(x)/cos(x) (coefficients of odd powers only).
%H A278194 Andrew Howroyd, <a href="/A278194/b278194.txt">Table of n, a(n) for n = 0..100</a>
%F A278194 a(n) = [x^(2*n+1)/(2*n+1)!] ( 1/5!*sin^5(x)/cos(x) ).
%F A278194 a(n) = (-1)^n*( 4^(n-2)*(4^n - 3) + 4^(n-1)*(4^(n+1) - 1)*Bernoulli(2*n + 2)/(n + 1) )/15.
%F A278194 a(n) = (-1)^n/(3!*2^6) * Sum_{k = 0..n} ( 25^(n-k) - 3*9^(n-k) + 2 )*binomial(2*n+1, 2*k)*2^(2*k)*E(2*k, 1/2), where E(n,x) is the Euler polynomial of order n.
%F A278194 a(n) = (-1)^n/(2^5*5!) * 2^(2*n+1)*( E(2*n+1, 3) - 5*E(2*n+1, 2) + 10*E(2*n+1, 1) - 10*E(2*n+1, 0) + 5*E(2*n+1, -1) - E(2*n+1, -2) ).
%F A278194 G.f. 1/5!*sin^5(x)/cos(x) = x^5/5! - 14*x^7/7! + 336*x^9/9! - 1408*x^11/11! + ....
%p A278194 seq((-1)^n*( 4^(n-2)*(4^n - 3) + 4^(n-1)*(4^(n+1) - 1)*bernoulli(2*n + 2)/(n + 1) )/15, n = 0..20);
%o A278194 (PARI) a(n)={my(m=2*n+1, A=O(x*x^m)); m!*polcoef(sin(x + A)^5/cos(x + A), m)/120} \\ _Andrew Howroyd_, May 04 2020
%Y A278194 Cf. A000364, A004174, A024235, A278079, A278080, A278195.
%K A278194 sign,easy
%O A278194 0,4
%A A278194 _Peter Bala_, Nov 15 2016
%E A278194 Terms a(15) and beyond from _Andrew Howroyd_, May 04 2020