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A122899
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Triangle with row sums counting directed animals.
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3
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1, 1, 1, 0, 4, 1, 0, 3, 9, 1, 0, 0, 18, 16, 1, 0, 0, 10, 60, 25, 1, 0, 0, 0, 80, 150, 36, 1, 0, 0, 0, 35, 350, 315, 49, 1, 0, 0, 0, 0, 350, 1120, 588, 64, 1, 0, 0, 0, 0, 126, 1890, 2940, 1008
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are A005773(n+1). Product of A007318 and A122899 is A103371.
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FORMULA
| Number triangle T(n,k)=sum{j=0..n, (-1)^(n-j)C(n,j)C(j+1,k+1)C(j,k)}
T(n,k) = C(n,k)*C(k+1,n-k). The columns of this triangle (ignoring leading zeros) give the rows of A123160. - Peter Bala (pbala(AT)toucansurf.com), Jan 24 2008
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EXAMPLE
| Triangle begins
1,
1, 1,
0, 4, 1,
0, 3, 9, 1,
0, 0, 18, 16, 1,
0, 0, 10, 60, 25, 1,
0, 0, 0, 80, 150, 36, 1,
0, 0, 0, 35, 350, 315, 49, 1,
0, 0, 0, 0, 350, 1120, 588, 64, 1,
0, 0, 0, 0, 126, 1890, 2940, 1008, 81, 1,
0, 0, 0, 0, 0, 1512, 7350, 6720, 1620, 100, 1
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CROSSREFS
| Cf. A123160.
Sequence in context: A062862 A084119 A166073 * A153661 A021713 A122388
Adjacent sequences: A122896 A122897 A122898 * A122900 A122901 A122902
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Sep 18 2006
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