A063263 Ninth column (k=8) of sextinomial array A063260.

3, 27, 125, 420, 1161, 2807, 6147, 12465, 23760, 43032, 74646, 124787, 202020, 317970, 488138, 732870, 1078497, 1558665, 2215875, 3103254, 4286579, 5846577, 7881525, 10510175, 13875030, 18145998, 23524452

Offset: 0

Author

Wolfdieter Lang, Jul 24 2001

Keywords

• nonn
• easy

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).

Crossrefs

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

Formula

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!.

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.

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