A348012 Invert transform of A037952.

1, 1, 2, 6, 15, 41, 107, 287, 758, 2022, 5362, 14276, 37916, 100874, 268084, 713006, 1895415, 5040433, 13400863, 35634419, 94745705, 251932417, 669862581, 1781165785, 4736000199, 12592950131, 33484024019, 89033206579, 236735594539

Offset: 0

Author

R. J. Mathar, Sep 24 2021

Keywords

• nonn
• easy

Comments

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.

Crossrefs

Row sums of A348013.

Formula

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

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.