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A348012
Invert transform of A037952.
1
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.
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
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Sep 24 2021
STATUS
approved