A092083 A convolution triangle of numbers obtained from A034789.

1, 21, 1, 546, 42, 1, 15561, 1533, 63, 1, 466830, 54054, 2961, 84, 1, 14471730, 1885338, 124740, 4830, 105, 1, 458960580, 65542932, 4977882, 236880, 7140, 126, 1, 14801478705, 2277656901, 192582117, 10661301, 399735, 9891, 147, 1

Offset

1,2

Comments

a(n,1) = A034789(n). a(n,m)=: s2(7; n,m), a member of a sequence of unsigned triangles including s2(2; n,m)=A007318(n-1,m-1) (Pascal's triangle). s2(3; n,m)= A035324(n,m), s2(4; n,m)= A035529(n,m), s2(5; n,m)= A048882(n,m), s2(6; n,m)= A049375.

Links

Table of n, a(n) for n=1..36.

Wolfdieter Lang, On generalizations of the Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Wolfdieter Lang, First 10 rows.

Formula

a(n, m) = 6*(6*(n-1)+m)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0; a(1, 1)=1.

G.f. for m-th column: ((-1+(1-36*x)^(-1/6))/6)^m.

Example

Triangle begins:
  {1};
  {21,1};
  {546,42,1};
  {15561,1533,63,1};
  ...

Crossrefs

Cf. A092086 (row sums), A092087 (alternating row sums).

Sequence in context: A260531 A252939 A132166 * A040435 A040434 A040437

Adjacent sequences: A092080 A092081 A092082 * A092084 A092085 A092086

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Mar 19 2004

Status

approved