A267007 - OEIS

%I #10 Aug 15 2019 23:47:24

%S 1,0,1,2,3,6,8,16,20,42,51,92,132,204,299,476,644,978,1488,2024,3048,

%T 4318,6248,8596,12555,17378,24740,34310,47940,65842,93221,125238,

%U 173848,239348,324724,445882,602140,816424,1101096,1495382,1991892,2684252,3598248

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

%H Vaclav Kotesovec, <a href="/A267007/b267007.txt">Table of n, a(n) for n = 0..10000</a>

%p b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0,

%p      `if`(n=0, 1, b(n, i-1)+(i-1)*b(n-i, min(n-i, i-1))))

%p     end:

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

%p seq(a(n), n=0..42);  # _Alois P. Heinz_, Aug 15 2019

%t nmax = 50; CoefficientList[Series[Product[1+(k-1)*x^k, {k, 1, nmax}], {x, 0, nmax}], x]

%t 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

%Y Cf. A022629, A162506, A267004, A267008.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Jan 08 2016