A008503 9-dimensional centered tetrahedral numbers.

1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184755, 352705, 646580, 1143780, 1960255, 3265757, 5303727, 8416837, 13079352, 19937632, 29860259, 43999449, 63865594, 91416974

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Bruno Berselli, 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).

Programs

GAP

B:=Binomial;; List([0..30], n-> B(n+10,10)-B(n,10) ); # G. C. Greubel, Nov 09 2019

Magma

B:=Binomial; [B(n+10,10)-B(n,10): n in [0..30]]; // G. C. Greubel, Nov 09 2019

Maple

seq(binomial(n+10,10)-binomial(n,10), n=0..30); # G. C. Greubel, Nov 09 2019

Mathematica

Table[Binomial[n + 10, 10] - Binomial[n, 10], {n, 0, 23}] (* Bruno Berselli, Mar 22 2012 *)

PARI

vector(31, n, b=binomial; b(n+9,10) - b(n-1,10) ) \\ G. C. Greubel, Nov 09 2019

Sage

b=binomial; [b(n+10,10)-b(n,10) for n in (0..30)] # G. C. Greubel, Nov 09 2019

Formula

G.f.: (1-x^10)/(1-x)^11 = (1+x)*(1+x+x^2+x^3+x^4)*(1-x+x^2-x^3+x^4)/(1-x)^10.

a(n) = (2*n + 1)*(5*n^8 + 20*n^7 + 1370*n^6 + 4040*n^5 + 56549*n^4 + 106388*n^3 + 425916*n^2 + 373392*n + 362880)/362880. [Bruno Berselli, Mar 22 2012]

a(n) = A001287(n+10)-A001287(n). - R. J. Mathar, Aug 10 2013