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Partial sums of A034263.
6

%I #26 Nov 08 2024 10:24:29

%S 1,10,49,168,462,1092,2310,4488,8151,14014,23023,36400,55692,82824,

%T 120156,170544,237405,324786,437437,580888,761530,986700,1264770,

%U 1605240,2018835,2517606,3115035,3826144,4667608,5657872,6817272,8168160,9735033,11544666

%N Partial sums of A034263.

%D Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

%H Harvey P. Dale, <a href="/A051947/b051947.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)*(2n+3)/3.

%F G.f.: (1+3*x)/(1-x)^7.

%F From _Amiram Eldar_, Feb 15 2022: (Start)

%F Sum_{n>=0} 1/a(n) = 2161/28 - 768*log(2)/7.

%F Sum_{n>=0} (-1)^n/a(n) = 192*Pi/7 - 624*log(2)/7 - 657/28. (End)

%t Nest[Accumulate,Range[1,160,4],5] (* _Vladimir Joseph Stephan Orlovsky_, Jan 29 2012 *)

%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,10,49,168,462,1092,2310},40] (* _Harvey P. Dale_, Nov 08 2024 *)

%Y Cf. A034263.

%Y Cf. A093561 ((4, 1) Pascal, column m=6).

%K easy,nonn,changed

%O 0,2

%A _Barry E. Williams_, Dec 21 1999

%E Corrected by _T. D. Noe_, Nov 09 2006