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 A002303 M5023 N2166 #30 Sep 15 2024 14:41:05 %S A002303 16,272,3968,56320,814080,12207360,191431680,3149752320,54428774400, %T A002303 987559372800,18797300121600,374883257548800,7822865085235200, %U A002303 170560590520320000,3879770715684864000,91945674412720128000 %N A002303 Generalized tangent numbers. %D A002303 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A002303 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %D A002303 Letterio Toscano, Sulla Derivata di Ordinen della Funzione tg(x), Tohoku Math. J., 42 (1936), 144-154. %F A002303 Ignoring the initial term a(4) = 16 and working with an offset of 0 the e.g.f. appears to be the rational function 16*(17+78*t+45*t^2)/(1-t)^10 = 272 + 3968*t + 56320*t^2/2! + ... . - _Peter Bala_, Apr 23 2012 %F A002303 This rational function occurs in the series reversion (x-t*tan(x))^(-1) = x/(1-t) + 2*t/(1-t)^4*x^3/3! + 8*t*(2+3*t)/(1-t)^7*x^5/5! + 16*t*(17+78*t+45*t^2)/(1-t)^10*x^7/7! + ..., which is the e.g.f. for the triangle A059419 read by diagonals. - _Peter Bala_, Apr 23 2012 %o A002303 (PARI) a(n, k)=if(k<0,0,if(n==1 && k==1,1,if(k>n,0,(k-1)*a(n-1,k-1)+(k+1)*a(n-1,k+1)))) %o A002303 for(n=0,25,print1(a(n+6, n)",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006 %Y A002303 Cf. A059419. %K A002303 nonn %O A002303 4,1 %A A002303 _N. J. A. Sloane_ %E A002303 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006