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%I #20 Sep 08 2022 08:44:58
%S 1,15,84,308,882,2142,4620,9108,16731,29029,48048,76440,117572,175644,
%T 255816,364344,508725,697851,942172,1253868,1647030,2137850,2744820,
%U 3488940,4393935,5486481,6796440,8357104
%N Partial sums of A051879.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H G. C. Greubel, <a href="/A050405/b050405.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) = binomial(n+5, 5)*(3*n + 2)/2.
%F G.f.: (1+8*x)/(1-x)^7.
%F E.g.f.: (240 +3360*x +6600*x^2 +4000*x^3 +950*x^4 +92*x^5 +3* x^6) *exp(x)/240. - _G. C. Greubel_, Oct 30 2019
%p seq(binomial(n+5, 5)*(3*n+2)/2, n=0..40); # _G. C. Greubel_, Oct 30 2019
%t Accumulate[Accumulate[Table[(n+1)(n+2)(n+3)(9n+4)/24,{n,0,40}]]] (* _Harvey P. Dale_, Aug 19 2012 *)
%o (PARI) vector(41, n, binomial(n+4, 5)*(3*n-1)/2) \\ _G. C. Greubel_, Oct 30 2019
%o (Magma) [Binomial(n+5, 5)*(3*n+2)/2: n in [0..40]]; // _G. C. Greubel_, Oct 30 2019
%o (Sage) [binomial(n+5, 5)*(3*n+2)/2 for n in (0..40)] # _G. C. Greubel_, Oct 30 2019
%o (GAP) List([0..40], n-> Binomial(n+5, 5)*(3*n+2)/2); # _G. C. Greubel_, Oct 30 2019
%Y Cf. A051879.
%Y Cf. A093644 ((9, 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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