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A002303
Generalized tangent numbers.
(Formerly M5023 N2166)
1
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.
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
KEYWORD
nonn
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 20 2006
STATUS
approved