A064054 Tenth column of trinomial coefficients.

5, 50, 266, 1016, 3139, 8350, 19855, 43252, 87802, 168168, 306735, 536640, 905658, 1481108, 2355962, 3656360, 5550755, 8260934, 12075184, 17363896, 24597925, 34370050, 47419905, 64662780, 87222720, 116470380, 154066125, 202008896, 262691396, 338962184

Offset: 0

Author

Wolfdieter Lang, Aug 29 2001

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

A005716 (ninth column), A111808.

Programs

Maple

A064054 := n -> GegenbauerC(`if`(9A064054(n)), n=5..20); # Peter Luschny, May 10 2016

Mathematica

Table[GegenbauerC[9, -n, -1/2], {n,5,50}] (* G. C. Greubel, Feb 28 2017 *)

PARI

for(n=0,25, print1(binomial(n+5,5)*(n^4 + 66*n^3 + 1307*n^2 + 8706*n + 15120) /(9!/5!), ", ")) \\ G. C. Greubel, Feb 28 2017

Formula

a(n) = A027907(n+5, 9).

a(n) = binomial(n+5, 5)*(n^4+66*n^3+1307*n^2+8706*n+15120) /(9!/5!).

G.f.: (1+x-x^2)*(5-5*x+x^2)/(1-x)^10, numerator polynomial is N3(9, x)= 5+0*x-9*x^2+6*x^3-x^4 from array A063420.

a(n) = A111808(n+5,9) for n>3. - Reinhard Zumkeller, Aug 17 2005

a(n) = 5*binomial(n+5,5) + 20*binomial(n+5,6) + 21*binomial(n+5,7) + 8*binomial(n+5,8) + binomial(n+5,9) (see our comment in A026729). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012

a(n) = GegenbauerC(N, -n, -1/2) where N = 9 if 9Peter Luschny, May 10 2016