A063267 Eighth column (k=7) of septinomial array A063265.

6, 33, 116, 325, 786, 1709, 3424, 6426, 11430, 19437, 31812, 50375, 77506, 116265, 170528, 245140, 346086, 480681, 657780, 888009, 1184018, 1560757, 2035776, 2629550, 3365830, 4272021, 5379588, 6724491, 8347650

Offset

0,1

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (8, -28, 56, -70, 56, -28, 8, -1).

Formula

a(n)= A063265(n+2, 7)= (n+1)*(n+2)*(n+10)*(n^4 + 22*n^3 + 193*n^2 + 792*n + 1512)/7!.

G.f.: (2-x)*(1-x+x^2)*(3-3*x+x^2)/(1-x)^8; the numerator polynomial is N7(7, x) = 6 - 15*x + 20*x^2 - 15*x^3 + 6*x^4 - x^5 from row n=7 of array A063266.

a(n) = binomial(n+7,n) - binomial(n+1,n). - Zerinvary Lajos, Jun 23 2006

a(n) = binomial(n+7,n) + binomial(n+6,n) + binomial(n+5,n) + binomial(n+4,n) + binomial(n+3,n) + binomial(n+2,n). - Zerinvary Lajos, Jun 23 2006

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8); a(0)=6, a(1)=33, a(2)=116, a(3)=325, a(4)=786, a(5)=1709, a(6)=3424, a(7)=6426. - Harvey P. Dale, Jan 06 2012

Maple

[seq((binomial(n+7, n)-binomial(n+1, n)), n=1..29)]; # Zerinvary Lajos, Jun 23 2006

Mathematica

Table[Binomial[n+7, n]-Binomial[n+1, n], {n, 30}] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 8, -1}, {6, 33, 116, 325, 786, 1709, 3424, 6426}, 30] (* Harvey P. Dale, Jan 06 2012 *)

Crossrefs

Cf. A000579 (column k=6 of A063265).

Sequence in context: A135526 A204185 A057818 * A082106 A297392 A263479

Adjacent sequences: A063264 A063265 A063266 * A063268 A063269 A063270

Keyword

nonn,easy

Author

Wolfdieter Lang, Jul 24 2001

Extensions

More terms from Zerinvary Lajos, Jun 23 2006

Status

approved