cp's OEIS Frontend

A160565 Diagonal sums of number triangle [k<=n]*C(n,2n-2k)2^(n-k)A000108(n-k).

%I A160565 #3 Mar 30 2012 18:59:25
%S A160565 1,0,1,2,1,6,9,12,41,60,121,310,505,1162,2577,4760,11089,23256,47089,
%T A160565 107274,223345,476366,1061017,2237796,4888313,10745748,23048169,
%U A160565 50792638,111180265,241786898,534219297
%N A160565 Diagonal sums of number triangle [k<=n]*C(n,2n-2k)2^(n-k)A000108(n-k).
%C A160565 Hankel transform is A160566(n+1).
%C A160565 a(0)=1 followed by A025252. [From _R. J. Mathar_, May 20 2009]
%F A160565 G.f.: (1-x^2-sqrt(1-2x^2-8x^3+x^4))/(4x^3);
%F A160565 G.f.: 1/(1-x^2-2*x^3/(1-x^2-2*x^3/(1-x^2-2*x^3/(1-x^2-2*x^3/(1-... (continued fraction).
%F A160565 a(n)=sum{k=0..floor(n/2), C(n-k,2n-4k)*2^(n-2k)*A000108(n-2k)};
%F A160565 a(n)=sum{k=0..n, C(n-k/2,2(n-k))*2^(n-k)*A000108(n-k)*(1+(-1)^k)/2};
%F A160565 a(n)=sum{k=0..n, C((n+k)/2,2k)*2^k*A000108(k)(1+(-1)^(n-k))/2}.
%F A160565 G.f.: (1/(1-x^2))c(2x^3/(1-x^2)^2) where c(x) is the g.f. of A000108. [From _Paul Barry_, May 20 2009]
%Y A160565 Cf.: A025250.
%K A160565 easy,nonn
%O A160565 0,4
%A A160565 _Paul Barry_, May 19 2009