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A051878 Partial sums of A051797.

%I A051878 #28 Sep 08 2022 08:44:59
%S A051878 1,13,63,203,518,1134,2226,4026,6831,11011,17017,25389,36764,51884,
%T A051878 71604,96900,128877,168777,217987,278047,350658,437690,541190,663390,
%U A051878 806715,973791,1167453,1390753,1646968,1939608,2272424,2649416,3074841,3553221,4089351,4688307,5355454,6096454
%N A051878 Partial sums of A051797.
%C A051878 Convolution of triangular numbers (A000217) and decagonal numbers (A001107). [_Bruno Berselli_, Jul 21 2015]
%D A051878 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%D A051878 Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.
%H A051878 <a href="/index/Ps#pyramidal_numbers">Index to sequences related to pyramidal numbers</a>
%H A051878 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A051878 a(n) = binomial(n+4, 4)*(8*n+5)/5.
%F A051878 G.f.: (1+7*x)/(1-x)^6.
%F A051878 E.g.f.: (120 +*1440*x +2280*x^2 +1040*x^3 +165*x^4 +8*x^5)*exp(x)/120. - _G. C. Greubel_, Aug 30 2019
%p A051878 seq((8*n+5)*binomial(n+4,4)/5, n=0..40); # _G. C. Greubel_, Aug 30 2019
%t A051878 Table[(8*n+5)*Binomial[n+4,4]/5, {n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 19 2011, modified by _G. C. Greubel_, Aug 30 2019 *)
%o A051878 (PARI) vector(40, n, (8*n-3)*binomial(n+3,4)/5) \\ _G. C. Greubel_, Aug 30 2019
%o A051878 (Magma) [(8*n+5)*Binomial(n+4,4)/5: n in [0..40]]; // _G. C. Greubel_, Aug 30 2019
%o A051878 (Sage) [(8*n+5)*binomial(n+4,4)/5 for n in (0..30)] # _G. C. Greubel_, Aug 30 2019
%o A051878 (GAP) List([0..40], n-> (8*n+5)*Binomial(n+4,4)/5); # _G. C. Greubel_, Aug 30 2019
%Y A051878 Cf. A000217, A001107, A051797.
%Y A051878 Cf. A093565 ((8, 1) Pascal, column m=5).
%K A051878 nonn,easy
%O A051878 0,2
%A A051878 _Barry E. Williams_, Dec 14 1999
%E A051878 Terms a(28) onward added by _G. C. Greubel_, Aug 30 2019