A111647 a(n) = A001541(n)*A001653(n+1)*A002315(n).

1, 105, 20213, 3998709, 791704585, 156753394977, 31036379835581, 6145046450172525, 1216688160731724433, 240898110778299543129, 47696609245941810082565, 9443687732585695622131557

Offset: 0

Author

Charlie Marion, Aug 24 2005

Keywords

• nonn
• easy

Examples

			a(1) = 105 = 3*5*7.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..434
• Index entries for linear recurrences with constant coefficients, signature (204,-1190,204,-1).

Crossrefs

Cf. A001541, A001653, A002315, A111648, A111649.

Programs

Magma

m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)))); // G. C. Greubel, Jul 15 2018

Mathematica

CoefficientList[Series[(1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)), {x, 0, 30}], x] (* G. C. Greubel, Jul 15 2018 *)

PARI

x='x+O('x^30); Vec((1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1))) \\ G. C. Greubel, Jul 15 2018

Formula

2*a(n) = A001109(3*n+1) + A001109(n+1).

a(n) = sqrt(A011900(2*n)*A046090(2*n)*A001109(2*n+1)).

a(n) = A001541(3*n) + 2*A001109(n)*A001541(n-1)*A001541(n).

For n>0, a(n) = A001652(3*n) - A053141(2*n)*A002315(n-1) - A001652(n-1).

G.f.: (1+3*x^3-17*x^2-99*x)/((x^2-6*x+1)*(x^2-198*x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

2*a(n) = A001109(n+1) + A097731(n) + 6*A097731(n-1). - R. J. Mathar, Jan 31 2024