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A064058
Ninth column of quintinomial coefficients.
2
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
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 29 2001
STATUS
approved