A392587 - OEIS

%I #14 Jan 17 2026 10:45:37

%S 1,6,21,56,128,270,552,1122,2280,4612,9243,18330,36027,70352,136752,

%T 264860,511280,983796,1887232,3610248,6889317,13117918,24928625,

%U 47287656,89551088,169324234,319698936,602813046,1135232744,2135427564,4012500479,7531906034,14124749751

%N Expansion of 1 / ((1-x)^3 - x^4)^2.

%H Seiichi Manyama, <a href="/A392587/b392587.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-13,0,5,-2,-1).

%F a(n) = Sum_{k=0..floor(n/4)} (k+1) * binomial(n-k+5,n-4*k).

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 13*a(n-4) + 5*a(n-6) - 2*a(n-7) - a(n-8).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/((1-x)^3-x^4)^2)

%Y Cf. A292324, A392552, A392588, A392589.

%Y Cf. A107068.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Jan 17 2026