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A064054 Tenth column of trinomial coefficients. 3
5, 50, 266, 1016, 3139, 8350, 19855, 43252, 87802, 168168, 306735, 536640, 905658, 1481108, 2355962, 3656360, 5550755, 8260934, 12075184, 17363896, 24597925, 34370050, 47419905, 64662780 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

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Last modified December 12 12:30 EST 2019. Contains 329958 sequences. (Running on oeis4.)