OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..576
FORMULA
G.f.: G(0)/(1-x^2)/(1+x) where G(k) = 1 - 2*x*(k+1)/((2*k+1)*(2*x*k-1) - x*(2*k+1)*(2*k+3)*(2*x*k-1)/(x*(2*k+3) - 2*(k+1)*(2*x*k+x-1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 04 2013.
G.f.: ( G(0) - 1 )/(1-x^2) where G(k) = 1 + (1-x)/(1-x*k)/(1-x/(x+(1-x)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 22 2013
a(n+1) - a(n) = A087650(n+1). - Vladimir Reshetnikov, Oct 29 2015
a(n) = Sum_{k=0..floor(n/2)} A000110(n-2*k). - Alois P. Heinz, Jun 17 2021
EXAMPLE
a(5) = 58 = 52 + 5 + 1.
MAPLE
b:= proc(n) option remember; `if`(n=0, 1,
add(b(n-j)*binomial(n-1, j-1), j=1..n))
end:
a:= n-> add(b(n-2*k), k=0..iquo(n, 2)):
seq(a(n), n=0..25); # Alois P. Heinz, Jun 17 2021
MATHEMATICA
a[n_] := Sum[BellB[n-2k], {k, 0, Quotient[n, 2]}];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 22 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Feb 09 2010
EXTENSIONS
More terms from Sergei N. Gladkovskii, Jan 04 2013
STATUS
approved