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

0,1

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).

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 9<n else 2*n-9. - Peter Luschny, May 10 2016

Maple

A064054 := n -> GegenbauerC(`if`(9<n, 9, 2*n-9), -n, -1/2):
seq(simplify(A064054(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 *)

Prog

(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

Crossrefs

A005716 (ninth column), A111808.

Sequence in context: A226548 A274064 A302695 * A301821 A301997 A227883

Adjacent sequences: A064051 A064052 A064053 * A064055 A064056 A064057

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 29 2001

Status

approved