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A079858
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E.g.f. 1/(cos(2*x) - sin(2*x)).
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3
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1, 2, 12, 88, 912, 11552, 176832, 3150208, 64188672, 1470996992, 37459479552, 1049279715328, 32063706796032, 1061443378552832, 37841217707753472, 1445427909919080448, 58892032991566036992, 2549444593020567683072
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: 1/(cos(2*x) - sin(2*x)).
a(n) = | 2*8^n*lerchphi(-1,-n,1/4) |. - Peter Luschny, Apr 27 2013
G.f.: 1/Q(0), where Q(k) = 1 - 2*x*(2*k+1) - 8*x^2*(k+1)^2/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Sep 27 2013
a(n) ~ 4 * n^(n+1/2) * (8/Pi)^n / (sqrt(Pi)*exp(n)). - Vaclav Kotesovec, Oct 07 2013
E.g.f.: 1/(1-2*x)*(1 + 2*x^2/((1-2*x)*W(0) - x )), where W(k) = x + (k+1)/( 1 - 2*x/( 2*k+3 - x*(2*k+3)/W(k+1) )); (continued fraction ). - Sergei N. Gladkovskii, Dec 27 2013
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MATHEMATICA
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CoefficientList[Series[1/(Cos[2*x]-Sin[2*x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 07 2013 *)
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PROG
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(PARI) a(n)=if(n<0, 0, n!*polcoeff(1/(cos(2*x+x*O(x^n))-sin(2*x+x*O(x^n))), n))
(Sage)
from mpmath import mp, lerchphi
mp.dps = 32; mp.pretty = True
def A079858(n): return abs(2*8^n*lerchphi(-1, -n, 1/4))
(PARI) x='x+O('x^66); v=Vec(serlaplace( 1/(cos(2*x)-sin(2*x)) ) ) \\ Joerg Arndt, Apr 27 2013
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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