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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);

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 November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)