A102473 Triangle read by rows. Let S(k) be the sequence defined by F(0)=0, F(1)=1, F(n-1) + (n+k)*F(n) = F(n+1). E.g. S(0) = 0,1,1,3,10,43,225,1393,9976,81201, ... Then S(0), S(1), S(2), ... are written next to each other, vertically, with the initial term of each on the next row down. The order of the terms in the rows are then reversed.

1, 1, 1, 1, 2, 3, 1, 3, 7, 10, 1, 4, 13, 30, 43, 1, 5, 21, 68, 157, 225, 1, 6, 31, 130, 421, 972, 1393, 1, 7, 43, 222, 931, 3015, 6961, 9976, 1, 8, 57, 350, 1807, 7578, 24541, 56660, 81201, 1, 9, 73, 520, 3193, 16485, 69133, 223884, 516901, 740785, 1, 10, 91, 738

Offset

1,5

Comments

For this triangle, the algorithm that generates the Bernoulli numbers gives 3/2, then 1/6, 1/24, ... 1/n!

T(n,n) = A001040(n); T(n,k) = A058294(n,k), k = 1..n. - Reinhard Zumkeller, Sep 14 2014

Links

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

Example

Triangle begins:
0
0 1
0 1 1
0 1 2 3
0 1 3 7 10
0 1 4 13 30 43
...
(the zeros are omitted).

Prog

(Haskell)
a102473 n k = a102473_tabl !! (n-1) !! (k-1)
a102473_row n = a102473_tabl !! (n-1)
a102473_tabl = [1] : [1, 1] : f [1] [1, 1] 2 where
   f us vs x = ws : f vs ws (x + 1) where
               ws = 1 : zipWith (+) ([0] ++ us) (map (* x) vs)
-- Reinhard Zumkeller, Sep 14 2014

Crossrefs

Mirror image of triangle in A102472.

Cf. A001040, A058294, A247365 (central terms).

Sequence in context: A071943 A357329 A062869 * A011117 A368401 A069269

Adjacent sequences: A102470 A102471 A102472 * A102474 A102475 A102476

Keyword

easy,nonn,tabl

Author

Russell Walsmith (russw(AT)lycos.com), Jan 09 2005

Extensions

Entry revised by N. J. A. Sloane, Jul 09 2005

Status

approved