A267007 Expansion of Product_{k>=1} (1 + (k-1)*x^k).

1, 0, 1, 2, 3, 6, 8, 16, 20, 42, 51, 92, 132, 204, 299, 476, 644, 978, 1488, 2024, 3048, 4318, 6248, 8596, 12555, 17378, 24740, 34310, 47940, 65842, 93221, 125238, 173848, 239348, 324724, 445882, 602140, 816424, 1101096, 1495382, 1991892, 2684252, 3598248

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Maple

b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,
     `if`(n=0, 1, b(n, i-1)+(i-1)*b(n-i, min(n-i, i-1))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..42);  # Alois P. Heinz, Aug 15 2019

Mathematica

nmax = 50; CoefficientList[Series[Product[1+(k-1)*x^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 50; poly = ConstantArray[0, nmax+1]; poly[[1]] = 1; poly[[2]] = 0; Do[Do[poly[[j+1]] += (k-1)*poly[[j-k+1]], {j, nmax, k, -1}]; , {k, 2, nmax}]; poly

Crossrefs

Cf. A022629, A162506, A267004, A267008.

Sequence in context: A268645 A047001 A174021 * A091070 A133586 A141348

Adjacent sequences: A267004 A267005 A267006 * A267008 A267009 A267010

Keyword

nonn

Author

Vaclav Kotesovec, Jan 08 2016

Status

approved