%I #4 Mar 14 2015 11:46:45
%S 1,4,10,33,68,123,226,342,547,778,1071,1412,1901,2392,2997,3762,4391,
%T 5534,6645,7632,9045,10546,11983,13870,16011,17672,20107,22986,25297,
%U 28100,31223,34468,38215,42194,45419,50134,54671,59154,64431,70022
%N Row 4 of table A162424.
%F a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^4 for n>=0 where S(x) = Sum_{n>=0} x^((n+1)(n+2)/2-1).
%e The coefficients in the 4th power of the series:
%e S = 1 + x^2 + x^5 + x^9 + x^14 + x^20 + x^27 + x^35 + x^44 +...
%e begin: [(1),(0,4),(0,6,4),(4,12,1,16),(6,16,12,12,12),...];
%e the sums of the grouped coefficients yield the initial terms of this sequence.
%o (PARI) {a(n)=local(S=sum(m=0,n+1,x^((m+1)*(m+2)/2-1))+O(x^((n+1)*(n+2)/2))); sum(m=n*(n+1)/2,n*(n+1)/2+n,polcoeff(S^4,m))}
%Y Cf. A162424, A162425, A162426, A162428, A162429, A162433 (variant).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 03 2009