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

0,3

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.

Links

Table of n, a(n) for n=0..28.

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.

Crossrefs

Row sums of A348013.

Sequence in context: A180666 A280788 A121328 * A139379 A236110 A362566

Adjacent sequences: A348009 A348010 A348011 * A348013 A348014 A348015

Keyword

nonn,easy

Author

R. J. Mathar, Sep 24 2021

Status

approved