A229151 a(n) = n^8*(5*n+4).

0, 9, 3584, 124659, 1572864, 11328125, 57106944, 224827239, 738197504, 2109289329, 5400000000, 12647173979, 27518828544, 56285419749, 109208390144, 202468359375, 360777252864, 620842412249, 1035876294144, 1681372741059, 2662400000000, 4122691670349

Offset: 0

Author

Alois P. Heinz, Sep 15 2013

Keywords

• nonn
• easy

Comments

Number of ascending runs in {1,...,n}^9.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Crossrefs

Row n=9 of A229079.

Programs

Maple

a:= n-> n^8*(5*n+4):
seq(a(n), n=0..40);

Mathematica

Table[n^8 (5n+4),{n,0,30}] (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{0,9,3584,124659,1572864,11328125,57106944,224827239,738197504,2109289329},30] (* Harvey P. Dale, Feb 11 2015 *)

Formula

G.f.: (x^8 +1526*x^7 +56856*x^6 +395866*x^5 +780950*x^4 +486474*x^3 +89224*x^2 +3494*x+9)*x / (x-1)^10.

a(0)=0, a(1)=9, a(2)=3584, a(3)=124659, a(4)=1572864, a(5)=11328125, a(6)=57106944, a(7)=224827239, a(8)=738197504, a(9)=2109289329, a(n)= 10*a(n-1)- 45*a(n-2)+120*a(n-3)-210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)- 45*a(n-8)+ 10*a(n-9)-a(n-10). - Harvey P. Dale, Feb 11 2015