A089514 Fourth column of triangle A089504.

1, 210, 31356, 4150440, 521757936, 64043874720, 7771495098816, 937759335004800, 112842062355914496, 13559707534436743680, 1628284591773850622976, 195461334300256627599360

Offset: 0

Author

Wolfdieter Lang, Dec 01 2003

Keywords

• nonn
• easy

Comments

Convolution of A089513 with powers of 120.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..480
• Index entries for linear recurrences with constant coefficients, signature (210,-12744,241920,-1036800).

Crossrefs

Cf. A089505, A089513.

Programs

Mathematica

CoefficientList[Series[1/((1-6x)(1-24x)(1-60x)(1-120x)),{x,0,20}],x] (* or *) LinearRecurrence[ {210,-12744,241920,-1036800},{1,210,31356,4150440},20] (* Harvey P. Dale, Mar 17 2023 *)

Formula

G.f.: 1/((1-3*2*1*x)*(1-4*3*2*x)*(1-5*4*3*x)*(1-6*5*4*x)).

a(n) = A089504(n+4, 4), n>=0.

a(n) = (1350*(6*5*4)^n - 950*(5*4*3)^n + 114*(4*3*2)^n - (3*2*1)^n)/513.