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 A162432 Row 3 of table A162430. 7

%I #7 Feb 07 2014 15:57:38

%S 1,6,13,25,39,52,81,97,129,154,187,234,250,321,337,406,468,493,579,

%T 613,699,766,811,918,979,1056,1141,1212,1357,1408,1485,1639,1698,1810,

%U 1908,2050,2152,2250,2398,2523,2629,2770,2934,2986,3219,3280,3522,3598,3739

%N Row 3 of table A162430.

%H Paul D. Hanna, <a href="/A162432/b162432.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)^3 for n>=0 where S(x) = Sum_{n>=0} x^(n(n+1)/2).

%e The coefficients in the cube of the series:

%e S = 1 + x + x^3 + x^6 + x^10 + x^15 + x^21 + x^28 + x^36 +...

%e begin: [(1),(3,3),(4,6,3),(6,9,3,7),(9,6,9,9,6),(6,15,9,7,12,3),...];

%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)}, k*(k+1)/2+k}]]; Table[t[3, k], {k, 0, 48}] (* _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^3,m))}

%Y Cf. A162430, A162431, A162433, A162434, A162435, A162426 (variant).

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 03 2009

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Last modified September 17 18:03 EDT 2024. Contains 375990 sequences. (Running on oeis4.)