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

Author

Benoit Cloitre, Mar 29 2002

Keywords

• easy
• nonn

Crossrefs

Cf. A001113, A049469, A348374.

Programs

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 *)

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

Extensions

Name clarified by Sean A. Irvine, Mar 19 2024

More terms from Amiram Eldar, May 05 2025