A230540 a(n) = 2*n*3^(2*n-1).

0, 6, 108, 1458, 17496, 196830, 2125764, 22320522, 229582512, 2324522934, 23245229340, 230127770466, 2259436291848, 22029503845518, 213516729579636, 2058911320946490, 19765548681086304, 189008059262887782, 1801135623563989452, 17110788423857899794

Offset: 0

Author

Bruno Berselli, Oct 23 2013

Keywords

• nonn
• easy

Comments

Arithmetic derivative of 9^n: a(n) = A003415(9^n).

Sum of reciprocals of a(n), for n>0: (3/2)*log(9/8).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (18,-81).

Crossrefs

Cf. A001019, A003415.

Cf. arithmetic derivative of k^n: A001787 (k=2), A027471 (k=3), A018215 (k=4), A053464 (k=5), A212700 (k=6), A027473 (k=7), A230539 (k=8), this sequence, A085708 (k=10), A081127 (k=11).

Programs

Magma

[2*n*3^(2*n-1): n in [0..20]];

Mathematica

Table[2 n 3^(2 n - 1), {n, 0, 20}]

PARI

a(n) = 2*n*3^(2*n-1); \\ Michel Marcus, Oct 23 2013

Formula

G.f.: 6*x/(1-9*x)^2.

a(n) = 6*A053540(n), with A053540(0)=0.