This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A273730 Square array read by antidiagonals: A(n,k) = number of permutations of n elements divided by the number of k-ary heaps on n+1 elements, n>=0, k>=1. 10
 1, 1, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 24, 1, 1, 1, 1, 3, 120, 1, 1, 1, 1, 2, 6, 720, 1, 1, 1, 1, 1, 3, 9, 5040, 1, 1, 1, 1, 1, 2, 4, 24, 40320, 1, 1, 1, 1, 1, 1, 3, 8, 45, 362880, 1, 1, 1, 1, 1, 1, 2, 4, 12, 108, 3628800, 1, 1, 1, 1, 1, 1, 1, 3, 5, 16, 189, 39916800 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened Wikipedia, D-ary heap FORMULA A(n,k) = A000142(n)/A273693(n+1,k). EXAMPLE Square array A(n,k) begins: :     1,  1,  1, 1, 1, 1, 1, 1, ... :     1,  1,  1, 1, 1, 1, 1, 1, ... :     2,  1,  1, 1, 1, 1, 1, 1, ... :     6,  2,  1, 1, 1, 1, 1, 1, ... :    24,  3,  2, 1, 1, 1, 1, 1, ... :   120,  6,  3, 2, 1, 1, 1, 1, ... :   720,  9,  4, 3, 2, 1, 1, 1, ... :  5040, 24,  8, 4, 3, 2, 1, 1, ... : 40320, 45, 12, 5, 4, 3, 2, 1, ... MAPLE with(combinat): b:= proc(n, k) option remember; local h, i, x, y, z;       if n<2 then 1 elif k<2 then k     else h:= ilog[k]((k-1)*n+1);          if k^h=(k-1)*n+1 then b((n-1)/k, k)^k*             multinomial(n-1, ((n-1)/k)\$k)        else x, y:=(k^h-1)/(k-1), (k^(h-1)-1)/(k-1);             for i from 0 do z:= (n-1)-(k-1-i)*y-i*x;               if y<=z and z<=x then b(y, k)^(k-1-i)*                  multinomial(n-1, y\$(k-1-i), x\$i, z)*                  b(x, k)^i*b(z, k); break fi             od       fi fi     end: A:= (n, k)-> n!/b(n+1, k): seq(seq(A(n, 1+d-n), n=0..d), d=0..14); MATHEMATICA multinomial[n_, k_List] := n!/Times @@ (k!); b[n_, k_] := b[n, k] = Module[{h, i, x, y, z}, Which[n<2, 1, k<2, k, True, h = Floor @ Log[k, (k - 1)*n + 1]; If [k^h == (k-1)*n+1, b[(n-1)/k, k]^k*multinomial[n-1, Array[(n-1)/k&, k]], {x, y} = {(k^h-1)/(k-1), (k^(h-1)-1)/(k-1)}; For[i = 0, True, i++, z = (n-1) - (k-1-i)*y - i*x; If[y <= z && z <= x, b[y, k]^(k-1-i)*multinomial[n-1, Join[Array[y&, k-1-i], Array[x&, i], {z}]] * b[x, k]^i*b[z, k] // Return]]]]]; A[n_, k_] :=  n!/b[n+1, k]; Table[A[n, 1+d-n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, Mar 13 2017, translated from Maple *) CROSSREFS Columns k=1-10 give: A000142, A133385, A273731, A273732, A273733, A273734, A273735, A273736, A273737, A273738. Cf. A273693. Sequence in context: A199958 A112734 A260685 * A326047 A320637 A280491 Adjacent sequences:  A273727 A273728 A273729 * A273731 A273732 A273733 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, May 28 2016 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 December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)