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A123490 Triangle whose k-th column satisfies a(n)=(k+3)*a(n-1)-(k+2)*a(n-2). +0
3
1, 2, 1, 4, 2, 1, 8, 5, 2, 1, 16, 14, 6, 2, 1, 32, 41, 22, 7, 2, 1, 64, 122, 86, 32, 8, 2, 1, 128, 365, 342, 157, 44, 9, 2, 1, 256, 1094, 1366, 782, 260, 58, 10, 2, 1 (list; table; graph; listen)
OFFSET

0,2

COMMENT

Column k has g.f. x^k*(1-x(1+k))/((1-x)*(1-x(2+k))). Row sums are A103439. Columns include A000079,A007051,A047849,A047850,A047851. Diagonal sums are A123491.

FORMULA

Number triangle T(n,k)=[k<=n]*((k+2)^(n-k)+k)/(k+1)

EXAMPLE

Triangle begins

1,

2, 1,

4, 2, 1,

8, 5, 2, 1,

16, 14, 6, 2, 1,

32, 41, 22, 7, 2, 1,

64, 122, 86, 32, 8, 2, 1,

128, 365, 342, 157, 44, 9, 2, 1,

256, 1094, 1366, 782, 260, 58, 10, 2, 1,

512, 3281, 5462, 3907, 1556, 401, 74, 11, 2, 1,

1024, 9842, 21846, 19532, 9332, 2802, 586, 92, 12, 2, 1

CROSSREFS

Cf. A047848.

Sequence in context: A106471 A054453 A109433 this_sequence A157028 A060637 A123486

Adjacent sequences: A123487 A123488 A123489 this_sequence A123491 A123492 A123493

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Oct 01 2006

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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