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%I #9 Feb 07 2014 15:51:08
%S 1,3,4,7,7,9,12,11,15,14,19,19,19,22,23,27,26,27,31,30,33,35,35,40,39,
%T 39,40,47,47,47,46,51,53,52,55,55,61,60,57,67,62,69,65,64,77,71,77,72,
%U 75,83,76,81,85,85,88,85,91,92,91,95,92,103,97,99,102,105,107,104,111
%N Row 2 of table A162430.
%H Paul D. Hanna, <a href="/A162431/b162431.txt">Table of n, a(n) for n = 0..254</a>
%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(n+1)/2).
%e The coefficients in the square of the series:
%e S = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 +...
%e begin: [(1),(2,1),(2,2,0),(3,2,0,2),(2,2,1,2,0),(2,4,0,2,0,1),...];
%e the sums of the grouped coefficients yield the initial terms of this sequence.
%t t[n_, k_] := Module[{s = Sum[x^(m*(m+1)/2), {m, 0, k+1}]+O[x]^((k+1)*(k+2)/2)}, Sum[Coefficient[s^n, x, m], {m, k*(k+1)/2, k*(k+1)/2+k}]]; Table[t[2, k], {k, 0, 68}] (* _Jean-François Alcover_, Nov 18 2013 *)
%o (PARI) {a(n)=local(S=sum(m=0,n+1,x^(m*(m+1)/2))+O(x^((n+1)*(n+2)/2))); sum(m=n*(n+1)/2,n*(n+1)/2+n,polcoeff(S^2,m))}
%Y Cf. A162430, A162432, A162433, A162434, A162435, A162425 (variant).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 03 2009
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