A059603 Expansion of (1+15*x+15*x^2+x^3)/(1-x)^12.

1, 27, 273, 1715, 8007, 30381, 98735, 284349, 742950, 1791426, 4037670, 8591154, 17392258, 33711510, 62886162, 113381398, 198287439, 337392405, 560004575, 908737245, 1444515345, 2253115995, 3453615945, 5209188075, 7740767580, 11344196916, 16411557852

Offset: 0

Author

Wolfdieter Lang, Feb 02 2001

Keywords

• nonn
• easy

Comments

a(n)= A038166(2*n).

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Programs

Mathematica

CoefficientList[Series[(1+15x+15x^2+x^3)/(1-x)^12,{x,0,40}],x] (* or *) LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{1,27,273,1715,8007,30381,98735,284349,742950,1791426,4037670,8591154},40] (* Harvey P. Dale, Jul 03 2017 *)

Formula

a(n)= binomial(n+8, 8)*(2*n+9)*(8*n^2+72*n+55)/(11*5*9).

G.f.:(1+15*x+15*x^2+x^3)/(1-x)^12.