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A034929 A triangle of Motzkin ballot numbers, read by rows. 1
1, 1, 1, 1, 2, 1, 1, 3, 3, 2, 1, 4, 6, 6, 4, 1, 5, 10, 13, 13, 9, 1, 6, 15, 24, 30, 30, 21, 1, 7, 21, 40, 59, 72, 72, 51, 1, 8, 28, 62, 105, 148, 178, 178, 127, 1, 9, 36, 91, 174, 276, 378, 450, 450, 323, 1, 10, 45, 128, 273, 480, 730, 980, 1158, 1158, 835, 1, 11, 55, 174, 410, 791 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Mirror image of A091836. Row sums are the Motzkin numbers (A001006). T(n,n-1)=A001006(n-2) (the Motzkin numbers). T(n,n-2)=A005554(n-1).

REFERENCES

M. Aigner, Motzkin numbers, Europ. J. Comb. 19 (1998), 663-675.

LINKS

Table of n, a(n) for n=1..72.

FORMULA

G.f.= 2(1+tz)/[1-2z+tz-2tz^2+sqrt(1-2tz-3t^2*z^2)].

EXAMPLE

Triangle begins:

[1],

[1, 1],

[1, 2, 1],

[1, 3, 3, 2],

[1, 4, 6, 6, 4],

[1, 5, 10, 13, 13, 9],

[1, 6, 15, 24, 30, 30, 21],

[1, 7, 21, 40, 59, 72, 72, 51]

CROSSREFS

Cf. A001006, A091836, A005554.

Sequence in context: A215065 A175424 A144401 * A099509 A153859 A131336

Adjacent sequences:  A034926 A034927 A034928 * A034930 A034931 A034932

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Edited by Emeric Deutsch, Mar 11 2004

STATUS

approved

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Last modified June 25 21:43 EDT 2019. Contains 324357 sequences. (Running on oeis4.)