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%I #2 Mar 30 2012 18:37:17
%S 1,2,3,4,7,7,8,11,13,13,16,15,19,22,21,23,22,29,27,31,30,29,39,34,37,
%T 37,40,47,41,45,46,47,53,48,55,57,53,58,57,65,62,61,65,68,71,71,69,74,
%U 75,77,74,79,87,85,82,81,91,90,93,89,93,96,95,101,100,103,101,104,107,109
%N Row 2 of table A162424.
%F a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^2 for n>=0 where S(x) = Sum_{n>=0} x^((n+1)(n+2)/2-1).
%e The coefficients in the square 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),(0,2),(0,1,2),(0,2,0,2),(1,2,0,0,4),(0,2,0,1,2,2),...];
%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^2,m))}
%Y Cf. A162424, A162426, A162427, A162428, A162429, A162431 (variant).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 03 2009
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