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