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 A162426 Row 3 of table A162424. 6

%I #2 Mar 30 2012 18:37:17

%S 1,3,6,13,24,34,49,69,94,117,148,174,211,249,298,331,366,439,498,535,

%T 591,670,733,792,880,939,1006,1123,1212,1270,1353,1456,1599,1648,1750,

%U 1896,1963,2127,2164,2379,2452,2545,2709,2848,2997,3094,3276,3385,3595

%N Row 3 of table A162424.

%F a(n) = Sum_{m=n(n+1)/2..n(n+1)/2+n} [x^m] S(x)^3 for n>=0 where S(x) = Sum_{n>=0} x^((n+1)(n+2)/2-1).

%e The coefficients in the cube 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),(0,3),(0,3,3),(1,6,0,6),(3,6,3,3,9),(1,12,0,6,9,6),...];

%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^3,m))}

%Y Cf. A162424, A162425, A162427, A162428, A162429; A162432 (variant).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 03 2009

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Last modified August 9 05:47 EDT 2024. Contains 375027 sequences. (Running on oeis4.)