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A071921
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Square array giving number of unimodal functions [n]->[m] for n>=0, m>=0, with a(0,m)=1 by definition, read by antidiagonals.
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1
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1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 4, 1, 0, 1, 4, 9, 7, 1, 0, 1, 5, 16, 22, 11, 1, 0, 1, 6, 25, 50, 46, 16, 1, 0, 1, 7, 36, 95, 130, 86, 22, 1, 0, 1, 8, 49, 161, 295, 296, 148, 29, 1, 0, 1, 9, 64, 252, 581, 791, 610, 239, 37, 1, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| If one uses a definition of unimodality that involves universal quantifiers on the domain of a function then a(0,m)=1 a priori.
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FORMULA
| a(n, m)=1 if n=0, m>=0, a(n, m)=sum_{k=0}^{m-1} binomial(2k+n-1, 2k) otherwise.
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CROSSREFS
| Sequence in context: A094266 A071569 A118340 * A003992 A171882 A118345
Adjacent sequences: A071918 A071919 A071920 * A071922 A071923 A071924
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Michele Dondi (bik.mido(AT)tiscalinet.it), Jun 14, 2002
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