A047689 -id:A047689 - cp's OEIS frontend

A047690 Denominators of coefficients in Taylor series for exp(cos(x)-1).

1, 2, 6, 720, 40320, 907200, 479001600, 87178291200, 5230697472000, 6402373705728000, 221172909834240000, 281000181944401920000, 620448401733239439360000, 403291461126605635584000000, 76222086152928465125376000000, 24113896346562823512391680000000

Offset: 0

N. J. A. Sloane

			1 - (1/2)*x^2 + (1/6)*x^4 - (31/720)*x^6 + (379/40320)*x^8 - (1639/907200)*x^10 + ...

CRC Standard Mathematical Tables and Formulae, 30th ed. 1996, p. 42.

Cf. A047689, A005046.

Cf. A097322.

A173197 a(0)=1, a(n)= 2+2^n/6+4*(-1)^n/3, n>0.

Original entry on oeis.org

1, 1, 4, 2, 6, 6, 14, 22, 46, 86, 174, 342, 686, 1366, 2734, 5462, 10926, 21846, 43694, 87382, 174766, 349526, 699054, 1398102, 2796206, 5592406, 11184814, 22369622, 44739246, 89478486, 178956974, 357913942, 715827886, 1431655766, 2863311534, 5726623062, 11453246126, 22906492246, 45812984494, 91625968982, 183251937966, 366503875926, 733007751854

Offset: 0

Paul Curtz, Feb 12 2010

Linked to Jacobsthal numbers (expansion of tan(x), a.k.a. Zag numbers) A000182=1,2,16,272,...: a(n+1)-2a(n) = -(-1)^n*(A000182(n) mod 10) = (-1,2,-6,2,-6,2,-6,...).
Cf. A173114, related to Euler (or secant, or Zig) numbers, A000364. a(n+1)+A010684=A001045.
First differences: 0,3,-2,4,0,8,8,24,... = 0,A154879 (third differences of A001045).
Main diagonal: A003945; first upper diagonal: -A171449; second: 4*A011782.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

a(n) = A093380(n+4), n>3.
a(n) = +2*a(n-1) +a(n-2) -2*a(n-3), n>3.
G.f.: 1-x*(-1-2*x+7*x^2)/((x-1)*(2*x-1)*(1+x)).
a(2n+2)+a(2n+3)=6*A047689.
a(2n)-a(2n-2) = 3,1,2,4,8,16,... = 3,A000079.

cp's OEIS Frontend

A047690 Denominators of coefficients in Taylor series for exp(cos(x)-1).

Views

Author

Keywords

Examples

References

Crossrefs

A173197 a(0)=1, a(n)= 2+2^n/6+4*(-1)^n/3, n>0.

Views

Author

Keywords

Comments

Links

Formula