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%I #20 Sep 08 2022 08:44:58
%S 1,16,91,336,966,2352,5082,10032,18447,32032,53053,84448,129948,
%T 194208,282948,403104,562989,772464,1043119,1388464,1824130,2368080,
%U 3040830,3865680,4868955,6080256,7532721,9263296
%N Partial sums of A051880.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H G. C. Greubel, <a href="/A050406/b050406.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = C(n+5, 5)*(5*n + 3)/3.
%F G.f.: (1+9*x)/(1-x)^7.
%F E.g.f.: (360 +5400*x +10800*x^2 +6600*x^3 +1575*x^4 +153*x^5 +5*x^6) *exp(x)/360. - _G. C. Greubel_, Oct 30 2019
%p seq(binomial(n+5,5)*(5*n+3)/3, n=0..40); # _G. C. Greubel_, Oct 30 2019
%t Nest[Accumulate[#]&,Table[n(n+1)(10n-7)/6,{n,0,50}],3] (* _Harvey P. Dale_, Nov 13 2013 *)
%o (PARI) vector(41, n, binomial(n+4,5)*(5*n-2)/3) \\ _G. C. Greubel_, Oct 30 2019
%o (Magma) [Binomial(n+5,5)*(5*n+3)/3: n in [0..40]]; // _G. C. Greubel_, Oct 30 2019
%o (Sage) [binomial(n+5,5)*(5*n+3)/3 for n in (0..40)] # _G. C. Greubel_, Oct 30 2019
%o (GAP) List([0..40], n-> Binomial(n+5,5)*(5*n+3)/3); # _G. C. Greubel_, Oct 30 2019
%Y Cf. A051880.
%Y Cf. A093645 ((10, 1) Pascal, column m=6).
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, Dec 21 1999
%E Corrected by _T. D. Noe_, Nov 09 2006
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