OFFSET
0,3
COMMENTS
Stirling transform of j-> ceiling(2^(j-2)). - Alois P. Heinz, Aug 25 2021
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..558
Sergey Kitaev, Partially Ordered Generalized Patterns, Discrete Math. 298 (2005), no. 1-3, 212-229.
FORMULA
a(n) = -2^(n-1) + 2*Sum_{i = 0..n-1} binomial(n-1,i) * a(i) with a(0) = 1. [It follows from Kitaev's recurrence for C_n on p. 220 of his paper.] - Petros Hadjicostas, Oct 30 2019
From Alois P. Heinz, Aug 25 2021: (Start)
G.f.: Sum_{k>=0} ceiling(2^(k-2))*x^k / Product_{j=1..k} (1-j*x).
a(n) = Sum_{j=0..n} Stirling2(n,j)*ceiling(2^(j-2)). (End)
MAPLE
b:= proc(n, m) option remember; `if`(n=0,
ceil(2^(m-2)), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..24); # Alois P. Heinz, Aug 25 2021
MATHEMATICA
b[n_, m_] := b[n, m] = If[n == 0,
Ceiling[2^(m-2)], m*b[n-1, m] + b[n-1, m+1]];
a[n_] := b[n, 0];
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Apr 15 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 16 2019
EXTENSIONS
More terms from Petros Hadjicostas, Oct 30 2019
STATUS
approved