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 A071920 Square array giving number of unimodal functions [n]->[m] for n>=0, m>=0, with a(0,m)=0 for all m>=0, read by antidiagonals. 14
 0, 0, 0, 0, 1, 0, 0, 2, 1, 0, 0, 3, 4, 1, 0, 0, 4, 9, 7, 1, 0, 0, 5, 16, 22, 11, 1, 0, 0, 6, 25, 50, 46, 16, 1, 0, 0, 7, 36, 95, 130, 86, 22, 1, 0, 0, 8, 49, 161, 295, 296, 148, 29, 1, 0, 0, 9, 64, 252, 581, 791, 610, 239, 37, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS If one uses a definition of unimodality that involves existential quantifiers on the domain of a function then a(0,m)=0 a priori. LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA a(n,m) = Sum_{k=0..m-1} binomial(n+2k-1, 2k) if n>0. EXAMPLE Square array a(n,m) begins: 0, 0, 0, 0, 0, 0, 0, 0, 0, ... 0, 1, 2, 3, 4, 5, 6, 7, 8, ... 0, 1, 4, 9, 16, 25, 36, 49, 64, ... 0, 1, 7, 22, 50, 95, 161, 252, 372, ... 0, 1, 11, 46, 130, 295, 581, 1036, 1716, ... 0, 1, 16, 86, 296, 791, 1792, 3612, 6672, ... 0, 1, 22, 148, 610, 1897, 4900, 11088, 22716, ... 0, 1, 29, 239, 1163, 4166, 12174, 30738, 69498, ... 0, 1, 37, 367, 2083, 8518, 27966, 78354, 194634, ... MAPLE a:= (n, m)-> `if`(n=0, 0, add(binomial(n+2*j-1, 2*j), j=0..m-1)): seq(seq(a(n, d-n), n=0..d), d=0..10); # Alois P. Heinz, Sep 21 2013 MATHEMATICA a[n_, m_] := Sum[Binomial[n+2*k-1, 2*k], {k, 0, m-1}]; a[0, _] = 0; Table[a[n-m, m], {n, 0, 10}, {m, n, 0, -1}] // Flatten (* Jean-François Alcover, Feb 25 2015 *) CROSSREFS Cf. A071921, A225010. Main diagonal is A088536. Sequence in context: A099423 A221515 A221984 * A306548 A320531 A345698 Adjacent sequences: A071917 A071918 A071919 * A071921 A071922 A071923 KEYWORD nonn,easy,tabl AUTHOR Michele Dondi (bik.mido(AT)tiscalinet.it), Jun 14 2002 STATUS approved

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Last modified April 23 06:04 EDT 2024. Contains 371906 sequences. (Running on oeis4.)