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A241188 Triangle T(n,s) of Dynkin type D_n read by rows (n >= 2, 0 <= s <= n). 0
1, 2, 1, 1, 3, 5, 5, 1, 4, 9, 16, 20, 1, 5, 14, 30, 55, 77, 1, 6, 20, 50, 105, 196, 294, 1, 7, 27, 77, 182, 378, 714, 1122, 1, 8, 35, 112, 294, 672, 1386, 2640, 4290, 1, 9, 44, 156, 450, 1122, 2508, 5148, 9867, 16445 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Table of n, a(n) for n=2..53.

M. A. A. Obaid, S. K. Nauman, W. M. Fakieh, C. M. Ringel, The numbers of support-tilting modules for a Dynkin algebra, 2014.

M. A. A. Obaid, S. K. Nauman, W. M. Fakieh, C. M. Ringel, The numbers of support-tilting modules for a Dynkin algebra, arXiv:1403.5827 [math.RT], 2014  and J. Int. Seq. 18 (2015) 15.10.6.

FORMULA

T(n,s) = [n+s-2,s] for 0 <= s < n, T(n,n) = [2n-2,n-2], where [t,s] stands for binomial(t,s)*(s+t)/t.

EXAMPLE

Triangle begins:

1, 2, 1,

1, 3, 5, 5,

1, 4, 9, 16, 20,

1, 5, 14, 30, 55, 77,

1, 6, 20, 50, 105, 196, 294,

1, 7, 27, 77, 182, 378, 714, 1122,

1, 8, 35, 112, 294, 672, 1386, 2640, 4290,

1, 9, 44, 156, 450, 1122, 2508, 5148, 9867, 16445,

...

CROSSREFS

See A009766 for the case of type A.

Diagonals give A029869, A051960, A029651, A051924. Row sums are also A051924.

Sequence in context: A187065 A174620 A210098 * A145236 A162206 A075248

Adjacent sequences:  A241185 A241186 A241187 * A241189 A241190 A241191

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Apr 24 2014

STATUS

approved

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Last modified August 16 00:25 EDT 2018. Contains 313782 sequences. (Running on oeis4.)