A316087 - OEIS

%I #22 Jul 04 2023 14:03:17

%S 1,-1,-3,-2,7,19,8,-53,-119,-18,387,727,-112,-2745,-4315,2238,18991,

%T 24715,-24296,-128461,-135023,219502,850635,688239,-1806560,-5515441,

%U -3116403,14022398,34994967,10783939,-104389592,-216919973,-5497639,752295022,1309660627

%N Expansion of 1/(1 + Sum_{k>=1} k^2 * x^k).

%H Seiichi Manyama, <a href="/A316087/b316087.txt">Table of n, a(n) for n = 0..3000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, -4, 1).

%F Convolution inverse of A253909.

%F G.f.: (x-1)^3/(x^3-4*x^2+2*x-1).

%F a(0) = 1; a(n) = -Sum_{k=1..n} k^2 * a(n-k). - _Ilya Gutkovskiy_, Feb 02 2021

%o (PARI) N=99; x='x+O('x^N); Vec(1/(1+sum(k=1, sqrtint(N), k^2*x^k)))

%Y 1/(1+ Sum_{k>=1} k^m * x^k): A163810 (m=1), this sequence (m=2), A316088 (m=3).

%Y Cf. A253909, A316086.

%K sign

%O 0,3

%A _Seiichi Manyama_, Jun 24 2018