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A102473
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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.
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5
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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
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OFFSET
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1,5
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COMMENTS
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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
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LINKS
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Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
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EXAMPLE
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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).
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PROG
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(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
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CROSSREFS
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Mirror image of triangle in A102472.
Cf. A001040, A058294, A247365 (central terms).
Sequence in context: A152821 A071943 A062869 * A011117 A069269 A193092
Adjacent sequences: A102470 A102471 A102472 * A102474 A102475 A102476
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Russell Walsmith (russw(AT)lycos.com), Jan 09 2005
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EXTENSIONS
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Entry revised by N. J. A. Sloane, Jul 09 2005
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STATUS
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approved
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