cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A348012 Invert transform of A037952.

Original entry on oeis.org

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

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Author

R. J. Mathar, Sep 24 2021

Keywords

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.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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