A064058 - OEIS

%I #16 Jul 31 2015 11:45:27

%S 1,15,85,320,951,2415,5475,11385,22110,40612,71214,120055,195650,

%T 309570,477258,718998,1061055,1537005,2189275,3070914,4247617,5800025,

%U 7826325,10445175,13798980,18057546,23422140

%N Ninth column of quintinomial coefficients.

%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) = A035343(n+2, 8) = binomial(n+4, 4)*(n^4+34*n^3+451*n^2+2874*n+1680)/(8!/4!).

%F G.f.: (1+6*x-14*x^2+11*x^3-3*x^4)/(1-x)^9; numerator polynomial is N5(8, x) from the array A063422.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) with a(0)=1, a(1)=15, a(2)=85, a(3)=320, a(4)=951, a(5)=2415, a(6)=5475, a(7)=11385, a(8)=22110. [From Harvey P. Dale, Oct 30 2011]

%F a(n) = C(n+2,2) + 12*C(n+2,3) + 31*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 A213887). - _Vladimir Shevelev_ and _Peter J. C. Moses_, Jun 22 2012

%t With[{c=8!/4!},Table[(Binomial[n+4,4](n^4+34n^3+451n^2+2874n+1680))/c, {n,0,30}]] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,15,85,320,951,2415,5475,11385,22110},30] (* _Harvey P. Dale_, Oct 30 2011 *)

%Y Cf. A064057 (eighth column), A000575 (tenth column).

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Aug 29 2001