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A052226 Partial sums of A050404.

%I A052226 #25 Sep 08 2022 08:44:59
%S A052226 1,15,92,372,1170,3102,7260,15444,30459,56485,99528,167960,273156,
%T A052226 430236,658920,984504,1438965,2062203,2903428,4022700,5492630,7400250,
%U A052226 9849060,12961260,16880175,21772881,27833040,35283952,44381832,55419320,68729232,84688560,103722729,126310119
%N A052226 Partial sums of A050404.
%D A052226 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%D A052226 Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.
%H A052226 G. C. Greubel, <a href="/A052226/b052226.txt">Table of n, a(n) for n = 0..1000</a>
%H A052226 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A052226 a(n) = (8*n+7)*C(n+6, 6)/7.
%F A052226 G.f.: (1+7*x)/(1-x)^8.
%F A052226 E.g.f.: (5040 +70560*x +158760*x^2 +117600*x^3 +36750*x^4 +5292*x^5 +343*x^6 +8*x^7)*exp(x)/5040. - _G. C. Greubel_, Aug 29 2019
%p A052226 seq((8*n+7)*Binomial(n+6, 6)/7, n=0..40); # _G. C. Greubel_, Aug 29 2019
%t A052226 Table[(8*n+7)*Binomial[n+6, 6]/7, {n,0,40}] (* _G. C. Greubel_, Aug 29 2019 *)
%t A052226 LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,15,92,372,1170,3102,7260,15444},40] (* _Harvey P. Dale_, Aug 12 2021 *)
%o A052226 (PARI) vector(40, n, (8*n-1)*binomial(n+5, 6)/7) \\ _G. C. Greubel_, Aug 29 2019
%o A052226 (Magma) [(8*n+7)*Binomial(n+6, 6)/7: n in [0..40]]; // _G. C. Greubel_, Aug 29 2019
%o A052226 (Sage) [(8*n+7)*binomial(n+6, 6)/7 for n in (0..40)] # _G. C. Greubel_, Aug 29 2019
%o A052226 (GAP) List([0..40], n-> (8*n+7)*Binomial(n+6, 6)/7); # _G. C. Greubel_, Aug 29 2019
%Y A052226 Cf. A050404.
%Y A052226 Cf. A093565 ((8, 1) Pascal, column m=7).
%K A052226 easy,nonn
%O A052226 0,2
%A A052226 _Barry E. Williams_, Jan 29 2000
%E A052226 Terms a(25) onward added by _G. C. Greubel_, Aug 29 2019