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A265707 Rectangular array A read by upward antidiagonals: A(n,m) is the number of surjective difunctional (regular) binary relations between an n-element set and an m-element set. 1
1, 1, 3, 1, 5, 7, 1, 9, 19, 15, 1, 17, 49, 65, 31, 1, 33, 127, 225, 211, 63, 1, 65, 337, 749, 961, 665, 127, 1, 129, 919, 2505, 3991, 3969, 2059, 255, 1, 257, 2569, 8525, 16201, 20237, 16129, 6305, 511, 1, 513, 7327, 29625, 65911, 97713 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A(n,m) is the number of surjective difunctional (regular) binary relations between an n-element set and an m-element set.

LINKS

Jasha Gurevich, Table of n, a(n) for n = 1..300

Chris Brink, Wolfram Kahl, Gunther Schmidt, Relational Methods in Computer Science, Springer Science & Business Media, 1997, p. 200.

J. Riguet, Relations binaires, fermetures, correspondances de Galois, Bulletin de la Société Mathématique de France (1948) Volume: 76, pp. 114-155.

Wikipedia, Binary relation

FORMULA

T(n, m) = Sum_{i=1..n} (Stirling2(m, i-1)* i! + Stirling2(m, i)* i! ) * Stirling2(n, i).

EXAMPLE

Array A begins

    1     1      1       1        1         1         1          1           1

    3     5      9      17       33        65       129        257         513

    7    19     49     127      337       919      2569       7327       21217

   15    65    225     749     2505      8525     29625     105149      380745

   31   211    961    3991    16201     65911    271561    1137991     4857001

   63   665   3969   20237    97713    464645   2214009   10657997    52034913

  127  2059  16129  100087   568177   3115519  16911049   91989367   504717697

  255  6305  65025  489149  3242265  20322605 124422105  756570029  4611314745

  511 19171 261121 2379511 18341401 130656871 896158921 6046077511 40608430681

MAPLE

sum((Stirling2(m, i-1)*factorial(i)+Stirling2(m, i)*factorial(i))*Stirling2(n, i), i = 1 .. n);

PROG

(PARI) T(n, m) = sum(i=1, n, (stirling(m, i-1, 2)*i! + stirling(m, i, 2)*i!)*stirling(n, i, 2));

CROSSREFS

Cf. A265417, A265706.

Sequence in context: A143524 A134249 A188509 * A336301 A188146 A001607

Adjacent sequences:  A265704 A265705 A265706 * A265708 A265709 A265710

KEYWORD

nonn,tabl

AUTHOR

Jasha Gurevich, Dec 14 2015

STATUS

approved

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Last modified August 5 22:41 EDT 2021. Contains 346488 sequences. (Running on oeis4.)