The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A245980 Number A(n,k) of pairs of endofunctions f, g on [n] satisfying g^k(f(i)) = f(i) for all i in [n]; square array A(n,k), n>=0, k>=0, read by antidiagonals. 14
 1, 1, 1, 1, 1, 16, 1, 1, 6, 729, 1, 1, 10, 87, 65536, 1, 1, 6, 213, 2200, 9765625, 1, 1, 10, 141, 8056, 84245, 2176782336, 1, 1, 6, 213, 6184, 465945, 4492656, 678223072849, 1, 1, 10, 87, 9592, 387545, 37823616, 315937195, 281474976710656 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Antidiagonals n = 0..80, flattened EXAMPLE Square array A(n,k) begins: 0 :        1,     1,      1,      1,      1,      1, ... 1 :        1,     1,      1,      1,      1,      1, ... 2 :       16,     6,     10,      6,     10,      6, ... 3 :      729,    87,    213,    141,    213,     87, ... 4 :    65536,  2200,   8056,   6184,   9592,   2200, ... 5 :  9765625, 84245, 465945, 387545, 682545, 159245, ... MAPLE with(numtheory): with(combinat): M:=multinomial: b:= proc(n, k, p) local l, g; l, g:= sort([divisors(p)[]]),       proc(k, m, i, t) option remember; local d, j; d:= l[i];         `if`(i=1, n^m, add(M(k, k-(d-t)*j, (d-t)\$j)/j!*          (d-1)!^j *M(m, m-t*j, t\$j) *g(k-(d-t)*j, m-t*j,         `if`(d-t=1, [i-1, 0], [i, t+1])[]), j=0..min(k/(d-t),         `if`(t=0, [][], m/t))))       end; g(k, n-k, nops(l), 0)     end: A:= (n, k)-> `if`(k=0, n^(2*n), add(b(n, j, k)*              stirling2(n, j)*binomial(n, j)*j!, j=0..n)): seq(seq(A(n, d-n), n=0..d), d=0..12); MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); M = multinomial; b[n_, k0_, p_] := Module[{l, g}, l = Sort[Divisors[p]]; g[k_, m_, i_, t_] := g[k, m, i, t] = Module[{d, j}, d = l[[i]]; If[i == 1, n^m, Sum[M[k, Join[{k - (d-t)*j}, Array[(d - t)&, j]]]/ j!*(d-1)!^j * M[m, Join[{m - t*j}, Array[t&, j]]]*If[d-t == 1, g[k - (d - t)*j, m - t*j, i-1, 0], g[k - (d-t)*j, m - t*j, i, t+1]], {j, 0, Min[k/(d-t), If[t == 0, Infinity, m/t]]}]]]; g[k0, n-k0, Length[l], 0]]; A[n_, k_] := If[k == 0, n^(2*n), Sum[b[n, j, k]* StirlingS2[n, j]*Binomial[n, j]*j!, {j, 0, n}]]; A[0, _] = 1; A[1, _] = 1; Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 12}] // Flatten (* Jean-François Alcover, Jan 27 2015, after Alois P. Heinz *) CROSSREFS Columns k=0-10 give: A062206, A239750, A239771, A241015, A245981, A245982, A245983, A245984, A245985, A245986, A245987. Main diagonal gives A245988. Cf. A245910. Sequence in context: A325938 A040258 A040257 * A040256 A245910 A133824 Adjacent sequences:  A245977 A245978 A245979 * A245981 A245982 A245983 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Aug 08 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 30 22:55 EDT 2020. Contains 333132 sequences. (Running on oeis4.)