The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A246070 Number A(n,k) of endofunctions f on [2n] satisfying f^k(i) = i for all i in [n]; square array A(n,k), n>=0, k>=0, read by antidiagonals. 7
 1, 1, 4, 1, 2, 256, 1, 3, 16, 46656, 1, 2, 50, 216, 16777216, 1, 3, 36, 1626, 4096, 10000000000, 1, 2, 56, 1440, 83736, 100000, 8916100448256, 1, 3, 16, 2688, 84624, 6026120, 2985984, 11112006825558016, 1, 2, 70, 720, 215760, 7675200, 571350096, 105413504, 18446744073709551616 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Antidiagonals n = 0..70, flattened EXAMPLE Square array A(n,k) begins: 0 : 1, 1, 1, 1, 1, 1, ... 1 : 4, 2, 3, 2, 3, 2, ... 2 : 256, 16, 50, 36, 56, 16, ... 3 : 46656, 216, 1626, 1440, 2688, 720, ... 4 : 16777216, 4096, 83736, 84624, 215760, 94816, ... 5 : 10000000000, 100000, 6026120, 7675200, 24899120, 11218000, ... 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, (2*n)^(2*n), b(2*n, n, k)): seq(seq(A(n, d-n), n=0..d), d=0..10); MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); M = multinomial; b[n_, k0_, p_] := Module[{l, g}, l = Divisors[p]; g[k_, m_, i_, t_] := g[k, m, i, t] = Module[{d, j}, d = l[[i]]; If[i == 1, If[m == 0, 1, n^m], Sum[M[k, Join[{k - (d - t)*j}, Table[d - t, {j}]]]/j!*If[j == 0, 1, (d - 1)!^j]*M[m, Join[{m - t*j}, Array[t&, j]]]*g[k - (d - t)*j, m - t*j, Sequence @@ If[d - t == 1, {i - 1, 0}, {i, t + 1}]], {j, 0, Min[k/(d - t), If[t == 0, {}, m/t]]}]]]; g[k0, n - k0, Length[l], 0]]; A[n_, k_] := If[k == 0, If[n == 0, 1, (2n)^(2n)], b[2*n, n, k]]; Table[A[n, d - n], {d, 0, 10}, {n, 0, d}] // Flatten (* Jean-François Alcover, May 27 2016, after Alois P. Heinz, updated Jan 01 2021 *) CROSSREFS Columns k=0-3 give: A085534, A062971, A245141, A245959. Main diagonal gives A246071. Cf. A246072 (the same for permutations). Sequence in context: A280284 A004161 A303141 * A202778 A025016 A355499 Adjacent sequences: A246067 A246068 A246069 * A246071 A246072 A246073 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Aug 12 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)