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%I #19 Jan 12 2017 14:28:28
%S 1,15,75,245,630,1386,2730,4950,8415,13585,21021,31395,45500,64260,
%T 88740,120156,159885,209475,270655,345345,435666,543950,672750,824850,
%U 1003275,1211301,1452465,1730575,2049720,2414280,2828936,3298680,3828825,4425015,5093235
%N a(n) = binomial(n+4,4)*(2*n+1).
%C Old name was: Partial sums of A051799.
%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)*(2n+1).
%F G.f.: (1+9*x)/(1-x)^6.
%t Nest[Accumulate[#]&,Table[n(n+1)(10n-7)/6,{n,0,50}],2] (* _Harvey P. Dale_, Nov 13 2013 *)
%Y Cf. A051799.
%Y Cf. A093645 ((10, 1) Pascal, column m=5).
%Y A diagonal of A280880.
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, Dec 14 1999
%E Name changed by _Alois P. Heinz_, Jan 09 2017
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