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 A226031 Number A(n,k) of unimodal functions f:[n]->[k*n]; square array A(n,k), n>=0, k>=0, read by antidiagonals. 3
 1, 1, 0, 1, 1, 0, 1, 2, 4, 0, 1, 3, 16, 22, 0, 1, 4, 36, 161, 130, 0, 1, 5, 64, 525, 1716, 791, 0, 1, 6, 100, 1222, 8086, 18832, 4900, 0, 1, 7, 144, 2360, 24616, 128248, 210574, 30738, 0, 1, 8, 196, 4047, 58730, 510664, 2072862, 2385644, 194634, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened FORMULA A(n,k) = Sum_{j=0..k*n-1} C(n+2*j-1,2*j), A(0,k) = 1. A(n,k) = A071921(n,k*n). EXAMPLE Square array A(n,k) begins:   1,   1,     1,      1,      1,       1, ...   0,   1,     2,      3,      4,       5, ...   0,   4,    16,     36,     64,     100, ...   0,  22,   161,    525,   1222,    2360, ...   0, 130,  1716,   8086,  24616,   58730, ...   0, 791, 18832, 128248, 510664, 1505205, ... MAPLE A:= (n, k)-> `if`(n=0, 1, add(binomial(n+2*j-1, 2*j), j=0..k*n-1)): seq(seq(A(n, d-n), n=0..d), d=0..10); MATHEMATICA A[n_, k_] := If[n==0, 1, Sum[Binomial[n + 2j - 1, 2j], {j, 0, k n - 1}]]; Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 10}] // Flatten (* Jean-François Alcover, Dec 20 2020, after Alois P. Heinz *) CROSSREFS Columns k=0-2 give: A000007, A088536, A226012. Rows n=0-2 give: A000012, A001477, A016742. Main diagonal gives: A227402. Cf. A071920. Sequence in context: A173004 A118343 A309148 * A308460 A244116 A138133 Adjacent sequences:  A226028 A226029 A226030 * A226032 A226033 A226034 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, May 23 2013 STATUS approved

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Last modified January 16 10:52 EST 2021. Contains 340206 sequences. (Running on oeis4.)