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%I #13 Dec 15 2015 10:06:51
%S 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,
%T 961,665,127,1,129,919,2505,3991,3969,2059,255,1,257,2569,8525,16201,
%U 20237,16129,6305,511,1,513,7327,29625,65911,97713
%N 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.
%C A(n,m) is the number of surjective difunctional (regular) binary relations between an n-element set and an m-element set.
%H Jasha Gurevich, <a href="/A265707/b265707.txt">Table of n, a(n) for n = 1..300</a>
%H Chris Brink, Wolfram Kahl, Gunther Schmidt, <a href="http://dx.doi.org/10.1007/978-3-7091-6510-2">Relational Methods in Computer Science</a>, Springer Science & Business Media, 1997, p. 200.
%H J. Riguet, <a href="http://www.numdam.org/item?id=BSMF_1948__76__114_0">Relations binaires, fermetures, correspondances de Galois</a>, Bulletin de la Société Mathématique de France (1948) Volume: 76, pp. 114-155.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Binary_relation#Difunctional">Binary relation</a>
%F T(n, m) = Sum_{i=1..n} (Stirling2(m, i-1)* i! + Stirling2(m, i)* i! ) * Stirling2(n, i).
%e Array A begins
%e 1 1 1 1 1 1 1 1 1
%e 3 5 9 17 33 65 129 257 513
%e 7 19 49 127 337 919 2569 7327 21217
%e 15 65 225 749 2505 8525 29625 105149 380745
%e 31 211 961 3991 16201 65911 271561 1137991 4857001
%e 63 665 3969 20237 97713 464645 2214009 10657997 52034913
%e 127 2059 16129 100087 568177 3115519 16911049 91989367 504717697
%e 255 6305 65025 489149 3242265 20322605 124422105 756570029 4611314745
%e 511 19171 261121 2379511 18341401 130656871 896158921 6046077511 40608430681
%p sum((Stirling2(m, i-1)*factorial(i)+Stirling2(m,i)*factorial(i))*Stirling2(n, i), i = 1 .. n);
%o (PARI) T(n, m) = sum(i=1, n, (stirling(m, i-1, 2)*i! + stirling(m, i, 2)*i!)*stirling(n, i, 2));
%Y Cf. A265417, A265706.
%K nonn,tabl
%O 1,3
%A _Jasha Gurevich_, Dec 14 2015
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