%I #9 Sep 25 2021 04:10:16

%S 1,1,2,6,15,41,107,287,758,2022,5362,14276,37916,100874,268084,713006,

%T 1895415,5040433,13400863,35634419,94745705,251932417,669862581,

%U 1781165785,4736000199,12592950131,33484024019,89033206579,236735594539

%N Invert transform of A037952.

%C Essentially the number of paths starting at the origin, consisting of n U or D steps or starting at the horizontal axis afresh after any number of steps, and never descending below the horizontal axis.

%F G.f.: 1/(1-g037952(x)) where g037952(x) = x +x^2 + 3*x^3+.. is the g.f. of A037952.

%F D-finite with recurrence n*a(n) +(-3*n+2)*a(n-1) +(-3*n+8)*a(n-2) +(11*n-46)*a(n-3) +2*(-n+12)*a(n-4) +4*(n-1)*a(n-5) +8*(-n+5)*a(n-6)=0.

%Y Row sums of A348013.

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Sep 24 2021