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a(n) = [x^n] 1/Product_{j=1..n} (1 - j^3*x).
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%I #21 Feb 19 2022 14:51:35

%S 1,1,73,28800,33120201,83648533275,393764054984212,

%T 3103381708489548640,37965284782803741391413,

%U 681476650259874114533077575,17184647574689079046814198039765,588057239856779143071625300022102376,26548105106818292578525347802793561068860

%N a(n) = [x^n] 1/Product_{j=1..n} (1 - j^3*x).

%H Alois P. Heinz, <a href="/A351800/b351800.txt">Table of n, a(n) for n = 0..149</a>

%F a(n) = Sum_{p in {1..n}^n : p_i <= p_{i+1}} Product_{j=1..n} p_j^3.

%F a(n) = A098436(2n-1,n-1) = A269948(2n,n).

%e a(2) = (1*1)^3 + (1*2)^3 + (2*2)^3 = 1 + 8 + 64 = 73.

%p b:= proc(n, k) option remember; `if`(k=0, 1,

%p add(b(j, k-1)*j^3, j=1..n))

%p end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..15);

%Y Cf. A000442, A001700, A007820, A088218, A098436, A269948, A298851, A351804.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Feb 19 2022