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A340952 Number of ways to write n as an ordered sum of 7 nonzero triangular numbers.

%I A340952 #8 Jan 31 2021 20:22:03
%S A340952 1,0,7,0,21,7,35,42,35,112,42,182,112,210,260,217,462,252,651,399,728,
%T A340952 777,672,1232,749,1533,1127,1659,1617,1792,2289,1890,2926,2212,3339,
%U A340952 2990,3584,3654,4046,4613,4263,5754,4487,6636,5733,6825,7014,7203,8617,7560,10087,8302
%N A340952 Number of ways to write n as an ordered sum of 7 nonzero triangular numbers.
%H A340952 Alois P. Heinz, <a href="/A340952/b340952.txt">Table of n, a(n) for n = 7..10000</a>
%F A340952 G.f.: (theta_2(sqrt(x)) / (2 * x^(1/8)) - 1)^7, where theta_2() is the Jacobi theta function.
%p A340952 b:= proc(n, k) option remember; local r, t, d; r, t, d:= $0..2;
%p A340952       if n=0 then `if`(k=0, 1, 0) else
%p A340952       while t<=n do r:= r+b(n-t, k-1); t, d:= t+d, d+1 od; r fi
%p A340952     end:
%p A340952 a:= n-> b(n, 7):
%p A340952 seq(a(n), n=7..58);  # _Alois P. Heinz_, Jan 31 2021
%t A340952 nmax = 58; CoefficientList[Series[(EllipticTheta[2, 0, Sqrt[x]]/(2 x^(1/8)) - 1)^7, {x, 0, nmax}], x] // Drop[#, 7] &
%Y A340952 Cf. A000217, A010054, A053603, A053604, A226252, A319817, A340949, A340950, A340951, A340953, A340954, A340955.
%K A340952 nonn
%O A340952 7,3
%A A340952 _Ilya Gutkovskiy_, Jan 31 2021