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A116950 Number of functional patterns on n elements; or digraphs with maximum outdegree 1, n arrows and every point connected to an arrow.

%I A116950 #15 Mar 13 2020 08:58:00
%S A116950 1,2,7,20,61,174,514,1478,4303,12437,36084,104494,303167,879283,
%T A116950 2552803,7413583,21544347,62635823,182199853,530228946,1543761513,
%U A116950 4496523995,13102414665,38193626823,111375529695,324891970936,948051861938,2767336312386,8080206646244
%N A116950 Number of functional patterns on n elements; or digraphs with maximum outdegree 1, n arrows and every point connected to an arrow.
%C A116950 A001372 counts functional patterns from a set with n elements to itself; A000041 (partition function) counts functional patterns from a set with n elements to a disjoint set; this is the general case where the range may overlap the domain but may also include other values.
%H A116950 Alois P. Heinz, <a href="/A116950/b116950.txt">Table of n, a(n) for n = 0..2127</a>
%F A116950 Euler transform of A002861(n) + A000081(n+1).
%F A116950 a(n) ~ c * d^n / sqrt(n), where d = A051491 = 2.95576528565199497471481752412..., c = 3.435908969217935496995961718... . - _Vaclav Kotesovec_, Sep 10 2014
%e A116950 For n=2 there are the following 7 digraphs:
%e A116950 o-+.o-+ o->o-+ o->o o-+.o->o o->o->o o->o o->o
%e A116950 ^.|.^.| ...^.| ^..| ^.|..... ....... ...^ ....
%e A116950 +-+.+-+ ...+-+ +--+ +-+..... ....... o--+ o->o
%t A116950 nmax = 750;
%t A116950 A002861 = Cases[Import["https://oeis.org/A002861/b002861.txt", "Table"], {_, _}][[;; nmax + 2, 2]];
%t A116950 A000081 = Cases[Import["https://oeis.org/A000081/b000081.txt", "Table"], {_, _}][[;; nmax + 2, 2]];
%t A116950 etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b];
%t A116950 b[n_] := A002861[[n]] + A000081[[n + 2]];
%t A116950 a = etr[b];
%t A116950 a[0] = 1;
%t A116950 a /@ Range[0, nmax](* _Jean-François Alcover_, Mar 13 2020 *)
%Y A116950 Cf. A000041, A001372, A002861, A000081.
%K A116950 easy,nice,nonn
%O A116950 0,2
%A A116950 _Franklin T. Adams-Watters_, Mar 29 2006