cp's OEIS Frontend

A280351 Expansion of Sum_{k>=0} (x/(1 - x))^(k^3).

%I A280351 #41 Jan 22 2024 15:22:41
%S A280351 1,1,1,1,1,1,1,1,2,9,37,121,331,793,1717,3433,6436,11441,19449,31825,
%T A280351 50389,77521,116281,170545,245158,346105,480701,657802,888058,1184419,
%U A280351 1564435,2063206,2799487,4272049,8544097,23535821,77331981,262534537,865287625,2720095405
%N A280351 Expansion of Sum_{k>=0} (x/(1 - x))^(k^3).
%C A280351 Number of compositions of n into a cube number of parts.
%H A280351 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A280351 a(0) = 1; a(n) = Sum_{k=1..floor(n^(1/3))} binomial(n-1, k^3-1) for n > 0. - _Jerzy R Borysowicz_, Dec 22 2022
%e A280351 a(9) = 9 because we have:
%e A280351 [1]  [9]
%e A280351 [2]  [2, 1, 1, 1, 1, 1, 1, 1]
%e A280351 [3]  [1, 2, 1, 1, 1, 1, 1, 1]
%e A280351 [4]  [1, 1, 2, 1, 1, 1, 1, 1]
%e A280351 [5]  [1, 1, 1, 2, 1, 1, 1, 1]
%e A280351 [6]  [1, 1, 1, 1, 2, 1, 1, 1]
%e A280351 [7]  [1, 1, 1, 1, 1, 2, 1, 1]
%e A280351 [8]  [1, 1, 1, 1, 1, 1, 2, 1]
%e A280351 [9]  [1, 1, 1, 1, 1, 1, 1, 2]
%p A280351 a := n -> ifelse(n = 0, 1, add(binomial(n - 1, k^3 - 1), k = 1..floor(n^(1/3)))):
%p A280351 seq(a(n), n = 0..39); # _Peter Luschny_, Dec 23 2022
%t A280351 nmax = 39; CoefficientList[Series[Sum[(x/(1 - x))^k^3, {k, 0, nmax}], {x, 0, nmax}], x]
%Y A280351 Cf. A000578, A052467, A103198, A280352.
%K A280351 nonn,easy
%O A280351 0,9
%A A280351 _Ilya Gutkovskiy_, Jan 01 2017
%E A280351 a(0)=1 prepended by _Alois P. Heinz_, Dec 17 2022