A089507 Second column of triangle A089504 and second column of array A078741 divided by 18.

1, 30, 756, 18360, 441936, 10614240, 254788416, 6115201920, 146766525696, 3522406694400, 84537821131776, 2028908069959680, 48693795855814656, 1168651113600245760, 28047626804770062336, 673143043784666480640

Offset: 0

Author

Wolfdieter Lang, Dec 01 2003

Keywords

• nonn
• easy

Comments

Convolution of A000400 (powers of 6) with A009968 (powers of 24).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..730
• Index entries for linear recurrences with constant coefficients, signature (30,-144).

Crossrefs

Cf. A089505, A089513, A089514.

Programs

Magma

[6^n*(4^(n+1)-1)/3: n in [0..15]]; // Vincenzo Librandi, Oct 18 2017

Mathematica

CoefficientList[Series[1/((1-6x)(1-24x)),{x,0,20}],x] (* or *) LinearRecurrence[{30,-144},{1,30},20] (* Harvey P. Dale, Sep 25 2017 *)

Formula

G.f.: 1/((1-3*2*1*x)*(1-4*3*2*x)).

a(n) = A089504(n+2, 2), n>=0.

a(n) = (4*(4*3*2)^n - (3*2*1)^n)/3 = (2^n)*(2^(2*(n+1))-1)*3^(n-1).

a(n) = 6^n*(4^(n+1)-1)/3. - Vincenzo Librandi, Oct 18 2017