A063417 Ninth column (k=8) of septinomial array A063265.

5, 36, 149, 470, 1251, 2954, 6371, 12789, 24210, 43637, 75438, 125801, 203294, 319545, 490058, 735182, 1081251, 1561914, 2219675, 3107664, 4291661, 5852396, 7888149, 10517675, 13883480, 18155475, 23535036

Offset

0,1

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) = A063265(n+2,8) = (n+1)*(n+2)*(n^6 +41*n^5 +701*n^4 +6439*n^3 +33930*n^2 +100008*n +100800)/8!.

G.f.: (5-9*x+5*x^2+5*x^3-9*x^4+5*x^5-x^6)/(1-x)^9; the numerator polynomial is N6(8,x) from row n=8 of array A063266.

a(n) = 5*C(n+2,2) + 21*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 A213889). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012

a(0)=5, a(1)=36, a(2)=149, a(3)=470, a(4)=1251, a(5)=2954, a(6)=6371, a(7)=12789, a(8)=24210, 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). - Harvey P. Dale, Aug 22 2012

Mathematica

Table[Total[Table[Binomial[n+2, i], {i, 2, 8}]{5, 21, 35, 35, 21, 7, 1}], {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {5, 36, 149, 470, 1251, 2954, 6371, 12789, 24210}, 30] (* Harvey P. Dale, Aug 22 2012 *)

Crossrefs

Cf. A063267.

Sequence in context: A027765 A196481 A096945 * A109726 A272561 A266097

Adjacent sequences: A063414 A063415 A063416 * A063418 A063419 A063420

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 24 2001

Status

approved