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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A089505, A089513, A089514.

Sequence in context: A273435 A259345 A181201 * A045689 A096722 A261030

Adjacent sequences: A089504 A089505 A089506 * A089508 A089509 A089510

Keyword

nonn,easy

Author

Wolfdieter Lang, Dec 01 2003

Status

approved