A002303 Generalized tangent numbers. (Formerly M5023 N2166)

16, 272, 3968, 56320, 814080, 12207360, 191431680, 3149752320, 54428774400, 987559372800, 18797300121600, 374883257548800, 7822865085235200, 170560590520320000, 3879770715684864000, 91945674412720128000

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

Table of n, a(n) for n=4..19.

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

Cf. A059419.

Sequence in context: A000487 A249391 A197622 * A158610 A221176 A231695

Adjacent sequences: A002300 A002301 A002302 * A002304 A002305 A002306

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006

Status

approved