login
Partial sums of A051798.
5

%I #20 Aug 06 2024 22:31:47

%S 1,14,69,224,574,1260,2478,4488,7623,12298,19019,28392,41132,58072,

%T 80172,108528,144381,189126,244321,311696,393162,490820,606970,744120,

%U 904995,1092546,1309959,1560664

%N Partial sums of A051798.

%C Convolution of triangular numbers (A000217) and 11-gonal numbers (A051682). [_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/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = C(n+4, 4)*(9n+5)/5.

%F G.f.: (1+8*x)/(1-x)^6.

%t Accumulate[Table[(n+1)(n+2)(n+3)(9n+4)/24,{n,0,40}]] (* _Harvey P. Dale_, Aug 19 2012 *)

%Y Cf. A051798; A000217, A051682.

%Y Cf. A093644((9, 1) Pascal, column m=5).

%Y Cf. A050405.

%K nonn,easy

%O 0,2

%A _Barry E. Williams_, Dec 14 1999