A323633 - OEIS

%I #14 Mar 22 2022 09:51:09

%S 1,-1,1,-1,1,-1,1,-1,0,1,-2,3,-4,5,-6,7,-7,6,-4,1,3,-8,14,-21,28,-34,

%T 38,-40,38,-31,18,2,-29,62,-99,139,-178,211,-232,234,-210,154,-62,-70,

%U 242,-449,680,-917,1135,-1303,1386,-1344,1136,-725,85,794,-1898,3183,-4571

%N Expansion of 1/Sum_{k>=0} x^(k^3).

%C Convolution inverse of A010057.

%H Seiichi Manyama, <a href="/A323633/b323633.txt">Table of n, a(n) for n = 0..10000</a>

%F a(0) = 1; a(n) = -Sum_{k=1..n} A010057(k) * a(n-k). - _Seiichi Manyama_, Mar 19 2022

%p a:=series(1/add(x^(k^3),k=0..100),x=0,59): seq(coeff(a,x,n),n=0..58); # _Paolo P. Lava_, Apr 02 2019

%t nmax = 58; CoefficientList[Series[1/Sum[x^k^3, {k, 0, nmax}], {x, 0, nmax}], x]

%t a[0] = 1; a[n_] := a[n] = -Sum[Boole[IntegerQ[k^(1/3)]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 58}]

%o (PARI) my(N=66, x='x+O('x^N)); Vec(1/sum(k=0, N^(1/3), x^k^3)) \\ _Seiichi Manyama_, Mar 19 2022

%o (PARI) a(n) = if(n==0, 1, -sum(k=1, n, ispower(k, 3)*a(n-k))); \\ _Seiichi Manyama_, Mar 19 2022

%Y Cf. A010057, A023358, A317665.

%K sign

%O 0,11

%A _Ilya Gutkovskiy_, Jan 21 2019