A187558 Triangle a(n,k) read by rows: product s(n,k)*s(n+1,k+1) of Stirling numbers of the first kind.

1, 0, 1, 0, 3, 1, 0, 22, 18, 1, 0, 300, 385, 60, 1, 0, 6576, 11250, 2975, 150, 1, 0, 211680, 444976, 165375, 14875, 315, 1, 0, 9408960, 23164848, 10992856, 1440600, 56350, 588, 1, 0, 552303360, 1543644432, 883573488, 151957281, 8890560, 175812, 1008, 1, 0, 41391544320, 128509156800, 85483976320, 18121263300, 1420415577, 42865200, 475020, 1620, 1

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..495

Formula

a(n,k) = A048994(n,k)*A048994(n+1,k+1) = A132393(n,k)*A132393(n+1,k+1).

Example

Triangle begins:
1
0,1
0,3,1
0,22,18,1
0,300,385,60,1
0,6576,11250,2975,150,1
0,211680,444976,165375,14875,315,1
0,9408960,23164848,10992856,1440600,56350,588,1
0,552303360,1543644432,883573488,151957281,8890560,175812,1008,1

Maple

seq(seq(combinat[stirling1](n, k)*combinat[stirling1](n+1, k+1), k=0..n), n=0..8);

Mathematica

Table[StirlingS1[n, k]StirlingS1[n + 1, k + 1], {n, 0, 8}, {k, 0, 8}]//MatrixForm

Prog

(Maxima) create_list(stirling1(n, k)*stirling1(n+1, k+1), n, 0, 10, k, 0, n);

Crossrefs

Sequence in context: A316773 A006837 A158782 * A327547 A233293 A361579

Adjacent sequences: A187555 A187556 A187557 * A187559 A187560 A187561

Keyword

nonn,easy,tabl

Author

Emanuele Munarini, Mar 11 2011

Status

approved