A079858 E.g.f. 1/(cos(2*x) - sin(2*x)).

1, 2, 12, 88, 912, 11552, 176832, 3150208, 64188672, 1470996992, 37459479552, 1049279715328, 32063706796032, 1061443378552832, 37841217707753472, 1445427909919080448, 58892032991566036992, 2549444593020567683072

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..385

Formula

E.g.f.: 1/(cos(2*x) - sin(2*x)).

a(n) = 2^n * A001586(n).

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

Mathematica

CoefficientList[Series[1/(Cos[2*x]-Sin[2*x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 07 2013 *)

Prog

(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))
[int(A079858(n)) for n in (0..17)]  # Peter Luschny, Apr 27 2013
(PARI)  x='x+O('x^66); v=Vec(serlaplace( 1/(cos(2*x)-sin(2*x)) ) ) \\ Joerg Arndt, Apr 27 2013

Crossrefs

Cf. A001586.

(-1)^(n*(n-1)/2)*a(n) gives the alternating row sums of A225118. - Wolfdieter Lang, Jul 12 2017

Sequence in context: A059435 A192621 A143923 * A224152 A174356 A355138

Adjacent sequences: A079855 A079856 A079857 * A079859 A079860 A079861

Keyword

nonn,easy

Author

Michael Somos, Jan 20 2003

Status

approved