Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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