OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{n >= 1} (-1 + Product_{k >= n} 1 + x^k).
G.f.: Sum_{n >= 1} n*x^n*Product_{k >= n+1} (1 + x^k). - Joerg Arndt, Jan 29 2011
G.f.: Sum_{k >= 1} x^(k*(k+1)/2)/(1 - x^k)/Product_{i = 1..k} (1 - x^i). - Vladeta Jovovic, Aug 10 2004
a(n) ~ exp(Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, May 20 2018
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i>n, 0, b(n, i+1)+b(n-i, i+1)))
end:
a:= n-> add(j*b(n-j, j+1), j=1..n):
seq(a(n), n=1..80); # Alois P. Heinz, Feb 03 2016
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i > n, 0, b[n, i + 1] + b[n - i, i + 1]]]; a[n_] := Sum[j*b[n - j, j + 1], {j, 1, n}]; Table[a[n], {n, 1, 80}] (* Jean-François Alcover, Jan 21 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 14 2004
EXTENSIONS
More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
STATUS
approved