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 A002303 Generalized tangent numbers. (Formerly M5023 N2166) 0
 16, 272, 3968, 56320, 814080, 12207360, 191431680, 3149752320, 54428774400, 987559372800, 18797300121600, 374883257548800, 7822865085235200, 170560590520320000, 3879770715684864000, 91945674412720128000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). Letterio Toscano, Sulla Derivata di Ordinen della Funzione tg(x), Tohoku Math. J., 42 (1936), 144-154. LINKS FORMULA 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 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 PROG (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)))) for(n=0, 25, print1(a(n+6, n)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006 CROSSREFS Sequence in context: A000487 A249391 A197622 * A158610 A221176 A231695 Adjacent sequences:  A002300 A002301 A002302 * A002304 A002305 A002306 KEYWORD nonn AUTHOR EXTENSIONS More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006 STATUS approved

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Last modified October 17 15:01 EDT 2019. Contains 328116 sequences. (Running on oeis4.)