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%I A008503 #28 Sep 08 2022 08:44:35
%S A008503 1,11,66,286,1001,3003,8008,19448,43758,92378,184755,352705,646580,
%T A008503 1143780,1960255,3265757,5303727,8416837,13079352,19937632,29860259,
%U A008503 43999449,63865594,91416974
%N A008503 9-dimensional centered tetrahedral numbers.
%H A008503 Bruno Berselli, <a href="/A008503/b008503.txt">Table of n, a(n) for n = 0..1000</a>
%H A008503 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A008503 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.
%F A008503 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]
%F A008503 a(n) = A001287(n+10)-A001287(n). - _R. J. Mathar_, Aug 10 2013
%p A008503 seq(binomial(n+10,10)-binomial(n,10), n=0..30); # _G. C. Greubel_, Nov 09 2019
%t A008503 Table[Binomial[n + 10, 10] - Binomial[n, 10], {n, 0, 23}] (* _Bruno Berselli_, Mar 22 2012 *)
%o A008503 (PARI) vector(31, n, b=binomial; b(n+9,10) - b(n-1,10) ) \\ _G. C. Greubel_, Nov 09 2019
%o A008503 (Magma) B:=Binomial; [B(n+10,10)-B(n,10): n in [0..30]]; // _G. C. Greubel_, Nov 09 2019
%o A008503 (Sage) b=binomial; [b(n+10,10)-b(n,10) for n in (0..30)] # _G. C. Greubel_, Nov 09 2019
%o A008503 (GAP) B:=Binomial;; List([0..30], n-> B(n+10,10)-B(n,10) ); # _G. C. Greubel_, Nov 09 2019
%K A008503 nonn,easy
%O A008503 0,2
%A A008503 _N. J. A. Sloane_

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