A299074 - OEIS

%I #14 Feb 02 2018 09:20:08

%S 1,33,853,20853,502789,12080901,290025541,6961116741,167069824837,

%T 4009693935429,96232763288389,2309586971953989,55430091245099845,

%U 1330322213391637317,31927733262454774597,766265599145247529797,18390374384563938483013,441368985260002510461765

%N Expansion of 1/((1-x)*(1-2*x)*(1-6*x)*(1-24*x)).

%H Colin Barker, <a href="/A299074/b299074.txt">Table of n, a(n) for n = 0..700</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (33,-236,492,-288).

%F O.g.f.: 1/((1 - x)*(1 - 2*x)(1 - 6*x)*(1 - 24*x)).

%F From _Colin Barker_, Feb 02 2018: (Start)

%F a(n) =  (-11 + 115*2^n - 759*6^n + 1920*24^n) / 1265.

%F a(n) = 33*a(n-1) - 236*a(n-2) + 492*a(n-3) - 288*a(n-4) for n>3. (End)

%o (PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, 4, (1-k!*x)))

%o (PARI) Vec(1/((1 - x)*(1 - 2*x)*(1 - 6*x)*(1 - 24*x)) + O(x^20)) \\ _Colin Barker_, Feb 02 2018

%Y Cf. A126646, A016200.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Feb 02 2018