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⇱ A062323 - OEIS

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A062323
Triangle with a(n,n)=1, a(n,k)=(n-1)*a(n-1,k)+a(n-2,k) for n>k.
3
1, 0, 1, 1, 1, 1, 2, 3, 2, 1, 7, 10, 7, 3, 1, 30, 43, 30, 13, 4, 1, 157, 225, 157, 68, 21, 5, 1, 972, 1393, 972, 421, 130, 31, 6, 1, 6961, 9976, 6961, 3015, 931, 222, 43, 7, 1, 56660, 81201, 56660, 24541, 7578, 1807, 350, 57, 8, 1, 516901, 740785, 516901, 223884
OFFSET
0,7
LINKS
FORMULA
a(n, k)=k*a(n, k+1)+a(n, k+2) for n>k.
EXAMPLE
Triangle starts:
[0] 1;
[1] 0, 1;
[2] 1, 1, 1;
[3] 2, 3, 2, 1;
[4] 7, 10, 7, 3, 1;
[5] 30, 43, 30, 13, 4, 1;
[6] 157, 225, 157, 68, 21, 5, 1;
[7] 972, 1393, 972, 421, 130, 31, 6, 1;
[8] 6961, 9976, 6961, 3015, 931, 222, 43, 7, 1;
PROG
(Haskell)
a062323 n k = a062323_tabl !! n !! k
a062323_row n = a062323_tabl !! n
a062323_tabl = map fst $ iterate f ([1], [0, 1]) where
f (us, vs) = (vs, ws) where
ws = (zipWith (+) (us ++ [0]) (map (* v) vs)) ++ [1]
where v = last (init vs) + 1
-- Reinhard Zumkeller, Mar 05 2013
CROSSREFS
Essentially the same as A058294, but more easy seen as a triangle. Columns include A001040, A001053, A058307, A058308, A058309. Other sequences appearing on the right hand side include A000012, A001477, A002061, A034262.
Sequence in context: A294408 A358605 A360026 * A291087 A020858 A090664
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, Jul 05 2001
STATUS
approved