A050404 - OEIS

%I #22 Sep 08 2022 08:44:58

%S 1,14,77,280,798,1932,4158,8184,15015,26026,43043,68432,105196,157080,

%T 228684,325584,454461,623238,841225,1119272,1469930,1907620,2448810,

%U 3112200,3918915,4892706,6060159,7450912

%N Partial sums of A051878.

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

%H G. C. Greubel, <a href="/A050404/b050404.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) = binomial(n+5, 5)*(4*n+3)/3.

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

%F E.g.f.: (360 +4680*x +9000*x^2 +5400*x^3 +1275*x^4 +123*x^5 +4*x^6 )*exp(x)/360. - _G. C. Greubel_, Aug 30 2019

%p seq((4*n+3)*binomial(n+5,5)/3, n=0..40); # _G. C. Greubel_, Aug 30 2019

%t Table[(4*n+3)*Binomial[n+5,5]/3, {n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 19 2011, modified by _G. C. Greubel_, Aug 30 2019 *)

%o (PARI) vector(40, n, (4*n-1)*binomial(n+4,5)/3) \\ _G. C. Greubel_, Aug 30 2019

%o (Magma) [(4*n+3)*Binomial(n+5,5)/3: n in [0..40]]; // _G. C. Greubel_, Aug 30 2019

%o (Sage) [(4*n+3)*binomial(n+5,5)/3 for n in (0..30)] # _G. C. Greubel_, Aug 30 2019

%o (GAP) List([0..40], n-> (4*n+3)*Binomial(n+5,5)/3); # _G. C. Greubel_, Aug 30 2019

%Y Cf. A051878.

%Y Cf. A093565 ((8, 1) Pascal, column m=6).

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, Dec 21 1999

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