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Search: id:A115195
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| A115195 |
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Triangle of numbers, called Y(1,2), related to generalized Catalan numbers A062992(n)=C(2;n+1)=A064062(n+1). |
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+0
7
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| 1, 2, 3, 4, 10, 13, 8, 28, 54, 67, 16, 72, 180, 314, 381, 32, 176, 536, 1164, 1926, 2307, 64, 416, 1488, 3816, 7668, 12282, 14589, 128, 960, 3936, 11568, 26904, 51468, 80646, 95235, 256, 2176, 10048, 33184, 86992, 189928, 351220, 541690, 636925, 512, 4864
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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This triangle Y(1,2) appears in the totally asymmetric exclusion process for the (unphysical) values alpha=1, beta=2. See the Derrida et al. refs. given under A064094, where the triangle entries are called Y_{N,K} for given alpha and beta.
The main diagonal (M=1) gives the generalized Catalan sequence C(2,n+1):=A064062(n+1).
The diagonal sequences give A064062(n+1), 2*A084076, 4*A115194, 8*A115202, 16*A115203, 32*A115204 for n+1>= M=1,..,6.
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LINKS
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W. Lang: First 10 rows.
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FORMULA
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G.f. m-th diagonal, m>=1: ((1 + 2*x*c(2*x))*(2*x*c(2*x))^m)/(2*x*(1+x)) with c(x) the o.g.f. of A000108 (Catalan).
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CROSSREFS
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Row sums give A115196.
Sequence in context: A005456 A100773 A131120 this_sequence A095384 A115899 A085934
Adjacent sequences: A115192 A115193 A115194 this_sequence A115196 A115197 A115198
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 23 2006
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