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A029582 E.g.f. sin(x) + cos(x) + tan(x). 3
1, 2, -1, 1, 1, 17, -1, 271, 1, 7937, -1, 353791, 1, 22368257, -1, 1903757311, 1, 209865342977, -1, 29088885112831, 1, 4951498053124097, -1, 1015423886506852351, 1, 246921480190207983617, -1, 70251601603943959887871, 1, 23119184187809597841473537 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

T. D. Noe, Table of n, a(n) for n = 0..100

FORMULA

G.f.: (1+x)/(1+x^2)+x/T(0) where T(k)=  1 - (k+1)*(k+2)*x^2/T(k+1) ; (recursively defined continued fraction). - Sergei N. Gladkovskii, Feb 12 2013

G.f.: (1+x)/(1+x^2)+x/G(0) where G(k) = 1 - 2*x^2*(4*k^2+4*k+1) - 4*x^4*(k+1)^2*(4*k^2+8*k+3)/G(k+1); (recursively defined continued fraction). - Sergei N. Gladkovskii, Feb 12 2013

MATHEMATICA

nn = 30; Range[0, nn]! CoefficientList[Series[Tan[x] + Sin[x] + Cos[x], {x, 0, nn}], x] (* T. D. Noe, Jul 16 2012 *)

PROG

(Sage) # Variant of an algorithm of L. Seidel (1877).

def A029582_list(n) :

    dim = 2*n; E = matrix(ZZ, dim); E[0, 0] = 1

    for m in (1..dim-1) :

        if m % 2 == 0 :

            E[m, 0] = 1;

            for k in range(m-1, -1, -1) :

                E[k, m-k] = E[k+1, m-k-1] - E[k, m-k-1]

        else :

            E[0, m] = 1;

            for k in range(1, m+1, 1) :

                E[k, m-k] = E[k-1, m-k+1] + E[k-1, m-k]

    return [(-1)^(k//2)*E[k, 0] for k in range(dim)]

A029582_list(15)  # Peter Luschny, Jul 14 2012

CROSSREFS

Cf. A009744, A099023.

Sequence in context: A236938 A079834 A256688 * A067095 A070888 A180849

Adjacent sequences:  A029579 A029580 A029581 * A029583 A029584 A029585

KEYWORD

sign

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 24 14:41 EST 2018. Contains 299623 sequences. (Running on oeis4.)