A008502 8-dimensional centered tetrahedral numbers.

1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48619, 92368, 167905, 293710, 496705, 815188, 1302499, 2031535, 3100240, 4638205, 6814522, 9847045, 14013220, 19662655, 27231610, 37259596

Offset

0,2

Links

Bruno Berselli, 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)

Formula

G.f.: (1-x^9 )/(1-x)^10 = (1+x+x^2)*(1+x^3+x^6) / (1-x)^9.

a(n) = 1 + n*(n+1)*(3*n^6+9*n^5+509*n^4+1003*n^3+11464*n^2+10964*n +36528)/13440. - R. J. Mathar, Nov 02 2011

Maple

seq(binomial(n+9, 9)-binomial(n, 9), n=0..30); # G. C. Greubel, Nov 09 2019

Mathematica

Table[Binomial[n + 9, 9] - Binomial[n, 9], {n, 0, 24}] (* Bruno Berselli, Mar 22 2012 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 10, 55, 220, 715, 2002, 5005, 11440, 24310}, 30] (* Harvey P. Dale, Jan 17 2016 *)

Prog

(PARI) vector(31, n, b=binomial; b(n+8, 9) - b(n-1, 9) ) \\ G. C. Greubel, Nov 09 2019
(Magma) B:=Binomial; [B(n+9, 9)-B(n, 9): n in [0..30]]; // G. C. Greubel, Nov 09 2019
(Sage) b=binomial; [b(n+9, 9)-b(n, 9) for n in (0..30)] # G. C. Greubel, Nov 09 2019
(GAP) B:=Binomial;; List([0..30], n-> B(n+9, 9)-B(n, 9) ); # G. C. Greubel, Nov 09 2019

Crossrefs

Sequence in context: A070212 A341207 A289380 * A008492 A023035 A128936

Adjacent sequences: A008499 A008500 A008501 * A008503 A008504 A008505

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved