A351800 a(n) = [x^n] 1/Product_{j=1..n} (1 - j^3*x).

1, 1, 73, 28800, 33120201, 83648533275, 393764054984212, 3103381708489548640, 37965284782803741391413, 681476650259874114533077575, 17184647574689079046814198039765, 588057239856779143071625300022102376, 26548105106818292578525347802793561068860

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..149

Formula

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

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

Example

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

Maple

b:= proc(n, k) option remember; `if`(k=0, 1,
      add(b(j, k-1)*j^3, j=1..n))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..15);

Crossrefs

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

Sequence in context: A070531 A274591 A232293 * A364440 A232366 A183490

Adjacent sequences: A351797 A351798 A351799 * A351801 A351802 A351803

Keyword

nonn

Author

Alois P. Heinz, Feb 19 2022

Status

approved