A063263 - OEIS

%I #18 Aug 19 2023 10:35:25

%S 3,27,125,420,1161,2807,6147,12465,23760,43032,74646,124787,202020,

%T 317970,488138,732870,1078497,1558665,2215875,3103254,4286579,5846577,

%U 7881525,10510175,13875030,18145998,23524452

%N Ninth column (k=8) of sextinomial array A063260.

%H Ray Chandler, <a href="/A063263/b063263.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

%F a(n) = A063260(n+2, 8) = (n+1)*(n+2)*(n+3)*(n^5+38*n^4+587*n^3+4678*n^2+19896*n+20160)/8!.

%F G.f.: (3-10*x^2+15*x^3-9*x^4+2*x^5)/(1-x)^9; the numerator polynomial is N6(8, x) from row n=8 of array A063261.

%F a(n) = 3*C(n+2,2) + 18*C(n+2,3) + 35*C(n+2,4) + 35*C(n+2,5) + 21*C(n+2,6) + 7*C(n+2,7) + C(n+2,8) (see comment in A213888). - _Vladimir Shevelev_ and _Peter J. C. Moses_, Jun 22 2012

%Y Cf. A062989, A063260, A063261, A063262, A063264, A213888.

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Jul 24 2001