A051879 - OEIS

%I #36 Feb 24 2026 08:21:05

%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 904995,1092546,1309959,1560664,1848344,2176944,2550680,2974048,3451833,3989118,4591293,5264064,6013462

%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 Kelvin Voskuijl, <a href="/A051879/b051879.txt">Table of n, a(n) for n = 0..10000</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) = C(n+4, 4)*(9*n+5)/5.

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

%F E.g.f.: exp(x)*(120 + 1560*x + 2520*x^2 + 1160*x^3 + 185*x^4 + 9*x^5)/120. - _Stefano Spezia_, Feb 23 2026

%t Table[((1 + n)(2 + n)(3 + n)(4 + n)(5 + 9 n))/120,{n,0,40}] (* _Harvey P. Dale_, Aug 19 2012, corrected by _Kelvin Voskuijl_, Feb 18 2026 *)

%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

%E More terms from _Kelvin Voskuijl_, Feb 18 2026