A064058 Ninth column of quintinomial coefficients.

1, 15, 85, 320, 951, 2415, 5475, 11385, 22110, 40612, 71214, 120055, 195650, 309570, 477258, 718998, 1061055, 1537005, 2189275, 3070914, 4247617, 5800025, 7826325, 10445175, 13798980, 18057546, 23422140

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Formula

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

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.

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]

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

Mathematica

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 *)

Crossrefs

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

Sequence in context: A091286 A176070 A160747 * A138322 A206170 A177882

Adjacent sequences: A064055 A064056 A064057 * A064059 A064060 A064061

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 29 2001

Status

approved