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A141686 Triangle T(n,m) = A008292(n,m)*binomial(n-1,m-1) read by rows. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 19 23:27 EDT 2021. Contains 345154 sequences. (Running on oeis4.)