A141686 Triangle T(n,m) = A008292(n,m)*binomial(n-1,m-1) read by rows.

1, 1, 1, 1, 8, 1, 1, 33, 33, 1, 1, 104, 396, 104, 1, 1, 285, 3020, 3020, 285, 1, 1, 720, 17865, 48320, 17865, 720, 1, 1, 1729, 90153, 546665, 546665, 90153, 1729, 1, 1, 4016, 409024, 4941104, 10933300, 4941104, 409024, 4016, 1, 1, 9117, 1722240, 38236128

Offset

1,5

Comments

Row sums are A104098(n-1). [Jun 30 2010]

Links

Reinhard Zumkeller, Rows n = 1..125 of table, flattened

Formula

T(n,m)=T(n,n+1-m).

Example

1;
1, 1;
1, 8, 1;
1, 33, 33, 1;
1, 104, 396, 104, 1;
1, 285, 3020, 3020, 285, 1;
1, 720, 17865, 48320, 17865, 720, 1;
1, 1729, 90153, 546665, 546665, 90153, 1729, 1;
1, 4016, 409024, 4941104, 10933300, 4941104, 409024, 4016, 1;
1, 9117, 1722240, 38236128, 165104604, 165104604, 38236128, 1722240, 9117, 1;

Mathematica

(*Recurrence*) A[n_, 1] := 1; A[n_, n_] := 1; A[n_, k_] := (n - k + 1)A[n - 1, k - 1] + k A[n - 1, k]; Table[Table[A[n, k]*Binomial[n - 1, k - 1], {k, 1, n}], {n, 1, 10}]; Flatten[%]

Prog

(Haskell)
a141686 n k = a141686_tabl !! (n-1) !! (k-1)
a141686_row n = a141686_tabl !! (n-1)
a141686_tabl = zipWith (zipWith (*)) a007318_tabl a008292_tabl
-- Reinhard Zumkeller, Apr 16 2014

Crossrefs

Cf. A008292.

Cf. A007318.

Sequence in context: A144439 A157208 A178347 * A185412 A157148 A220595

Adjacent sequences: A141683 A141684 A141685 * A141687 A141688 A141689

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Sep 08 2008

Extensions

keyword:tabl inserted, indices corrected by the Assoc. Eds. of the OEIS, Jun 30 2010

Status

approved