A068878 Denominators of nonzero terms in the expansion of sin(x)+exp(x)-1-2*x.

2, 24, 60, 720, 40320, 181440, 3628800, 479001600, 3113510400, 87178291200, 20922789888000, 177843714048000, 6402373705728000, 2432902008176640000, 25545471085854720000, 1124000727777607680000, 620448401733239439360000, 7755605021665492992000000, 403291461126605635584000000

Offset

1,1

Links

Table of n, a(n) for n=1..19.

Formula

a(3k+1)=(4k+2)!, a(3k+2)=(4k+4)!, a(3k+3)=(4k+5)!/2.

Sum_{n>=1} 1/a(n) = e + sin(1) - 3 = A001113 + A049469 - 3 = A348374 - 3. - Amiram Eldar, May 05 2025

Mathematica

Select[CoefficientList[Series[Sin[x] + Exp[x] - 1 - 2 x, {x, 0, 25}], x], # != 0 &] // Denominator
(* second program: *)
a[n_] := Switch[Mod[n, 3], 1, ((4*n+2)/3)!, 2, ((4*n+4)/3)!, 0, ((4*n+3)/3)!/2]; Array[a, 17] (* Amiram Eldar, May 05 2025 *)

Crossrefs

Cf. A001113, A049469, A348374.

Sequence in context: A079608 A257663 A292162 * A100918 A152965 A345692

Adjacent sequences: A068875 A068876 A068877 * A068879 A068880 A068881

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 29 2002

Extensions

Name clarified by Sean A. Irvine, Mar 19 2024

More terms from Amiram Eldar, May 05 2025

Status

approved