A392584 - OEIS

%I #13 Jan 17 2026 11:01:57

%S 1,6,21,58,144,342,795,1818,4095,9104,20028,43692,94661,203886,436905,

%T 932070,1980648,4194306,8854639,18641346,39146835,82021948,171500436,

%U 357913944,745654041,1550960406,3221225469,6681060242,13839339072,28633115310,59175104963,122167958634

%N Expansion of 1 / ((1-x)^3 - x^3)^2.

%H Seiichi Manyama, <a href="/A392584/b392584.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,22,-21,12,-4).

%F a(n) = Sum_{k=0..floor(n/3)} (k+1) * binomial(n+5,n-3*k).

%F a(n) = 6*a(n-1) - 15*a(n-2) + 22*a(n-3) - 21*a(n-4) + 12*a(n-5) - 4*a(n-6).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x)^3-x^3)^2)

%Y Cf. A024495.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jan 17 2026