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%I #26 Aug 01 2017 11:50:37
%S 1,10,45,130,300,612,1105,1830,2925,4420,6341,9000,12325,16290,21645,
%T 27932,34980,44370,54900,66430,81702,98050,115440,138330,162565,
%U 187800,220545,254800,289265,334890,382058,427350,488700,550420,609960,691812,770185,845750,949365,1049400,1145580,1274580
%N Number of ways of writing n as the sum of 10 triangular numbers from A000217.
%H Seiichi Manyama, <a href="/A226254/b226254.txt">Table of n, a(n) for n = 0..10000</a>
%H K. Ono, S. Robins and P. T. Wahl, <a href="http://www.mathcs.emory.edu/~ono/publications-cv/pdfs/006.pdf">On the representation of integers as sums of triangular numbers</a>, Aequationes mathematicae, August 1995, Volume 50, Issue 1-2, pp 73-94. Case k=10, Theorem 6.
%F G.f. is 10th power of g.f. for A010054.
%F a(n) = (A050456(4*n+5) - A030212(4*n+5))/640. See the Ono et al. link, case k=10, Theorem 6. - _Wolfdieter Lang_, Jan 13 2017
%F a(0) = 1, a(n) = (10/n)*Sum_{k=1..n} A002129(k)*a(n-k) for n > 0. - _Seiichi Manyama_, May 06 2017
%F G.f.: exp(Sum_{k>=1} 10*(x^k/k)/(1 + x^k)). - _Ilya Gutkovskiy_, Jul 31 2017
%Y Cf. A000217, A030212, A050456.
%Y Number of ways of writing n as a sum of k triangular numbers, for k=1,...: A010054, A008441, A008443, A008438, A008439, A008440, A226252, A007331, A226253, A226254, A226255, A014787, A014809.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jun 01 2013
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