OFFSET
1,2
COMMENTS
a(n+1)/a(n) tends to 3.
a(n)/A007051(n) tends to Product_{k>=1} (1-1/((3^k + 1)/2)). To observe the asymptote one needs 1000 or more decimal digits of the constant c=Product_{k>=1} (1-1/((3^k + 1)/2)). - Mats Granvik, Jan 02 2015
FORMULA
a(n) ~ Product_{k>=1} (1-1/((3^k + 1)/2))*A007051(n). - Mats Granvik, Jan 01 2015
EXAMPLE
a(25)/A007051(24) = 50658893073/141214768241 = 0.35873650967258963431... which is close to 0.35792312728995990302591...
MATHEMATICA
Clear[t]; nn = 25; t[n_, 1] = 1; t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k - 1], {i, 1, k - 1}] + Sum[t[n - i, k], {i, 1, k - 1}], 0]; Table[Sum[t[n, k], {k, 1, n}], {n, 1, nn}](* Mats Granvik, Jan 02 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mats Granvik, Apr 08 2010
STATUS
approved