OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..588
FORMULA
a(n) = Sum_{k=0..n} S2(k,n-k)*2^(2k-n) where S2(n,k)=A048993(n,k).
a(n) = Sum_{k=0..floor(n/2)} S2(n-k,k)*2^(n-2k) where S2(n,k)=A048993(n,k).
Let E(x) = Sum_{k>=0} x^(2*k)/Product_{j=1..k} (1 - j*2*x), then E(x) = 1 + x^2/(U(0)-x^2), where U(k) = (x-1)^2 - 2*k*x + x^2*(2*k*x + 2*x - 1)/U(k+1); (continued fraction). - Sergei N. Gladkovskii, Jun 26 2012
G.f.: 1 + x*(G(0) - 1)/(x-1) where G(k) = 1 - x/(1-x*(2*k+2))/(1-x/(x-1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jan 16 2013
PROG
(PARI) a(n) = sum(k=0, n\2, 2^(n-2*k)*stirling(n-k, k, 2)); \\ Seiichi Manyama, Apr 08 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 19 2006
STATUS
approved