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%I #15 Sep 08 2022 08:45:01
%S 1,14,95,440,1595,4862,13013,31460,70070,145860,286858,537472,965770,
%T 1673140,2806870,4576264,7272991,11296450,17185025,25654200,37642605,
%U 54367170,77388675,108689100,150762300,206719656,280412484,376573120
%N a(n) = (5*n + 9)*binomial(n+8, 8)/9.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H G. C. Greubel, <a href="/A055844/b055844.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F a(n) = (5*n+9)*binomial(n+8, 8)/9.
%F G.f.: (1+4*x)/(1-x)^10.
%F From _G. C. Greubel_, Jan 21 2020: (Start)
%F a(n) = 5*binomial(n+9, 9) - 4*binomial(n+8, 8).
%F E.g.f.: (362880 +4717440*x +12337920*x^2 +11854080*x^3 +5292000*x^4 +1227744*x^5 +155232*x^6 +10656*x^7 +369*x^8 +5*x^9)*exp(x)/362880. (End)
%p seq((5*n+9)*binomial(n+8, 8)/9, n=0..30); # _G. C. Greubel_, Jan 21 2020
%t Table[5*Binomial[n+9,9] -4*Binomial[n+8,8], {n,0,30}] (* _G. C. Greubel_, Jan 21 2020 *)
%o (PARI) vector(31, n, (5*n+4)*binomial(n+7, 8)/9) \\ _G. C. Greubel_, Jan 21 2020
%o (Magma) [(5*n+9)*Binomial(n+8, 8)/9: n in [0..30]]; // _G. C. Greubel_, Jan 21 2020
%o (Sage) [(5*n+9)*binomial(n+8, 8)/9 for n in (0..30)] # _G. C. Greubel_, Jan 21 2020
%o (GAP) List([0..30], n-> (5*n+9)*Binomial(n+8, 8)/9); # _G. C. Greubel_, Jan 21 2020
%Y Cf. A052255.
%Y Cf. A093562 ((5, 1) Pascal, column m=9).
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, May 30 2000
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