A089513 Third column of triangle A089504.

1, 90, 6156, 387720, 23705136, 1432922400, 86230132416, 5179923146880, 310942155338496, 18660051727004160, 1119687641441381376, 67183287394552842240, 4031045937469026349056, 241863924899255181189120

Offset: 0

Author

Wolfdieter Lang, Dec 01 2003

Keywords

• nonn
• easy

Comments

Convolution of A089507 with powers of 60.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..562
• Index entries for linear recurrences with constant coefficients, signature (90,-1944,8640).

Crossrefs

Cf. A089505, A089507, A089514.

Programs

Mathematica

CoefficientList[Series[1/(1-90 x+1944 x^2-8640 x^3),{x,0,20}],x] (* or *) LinearRecurrence[{90,-1944,8640},{1,90,6156},20] (* Harvey P. Dale, Jul 07 2021 *)

Formula

G.f.: 1/((1-3*2*1*x)*(1-4*3*2*x)*(1-5*4*3*x)).

a(n)=A089504(n+3, 3), n>=0.

a(n)= (50*(5*4*3)^n - 24*(4*3*2)^n + (3*2*1)^n)/27 = (6^n)*(5*10^(n+1) - 3*2^(2*n+3) + 1)/27.