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A106579
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Triangular array associated with Schroeder numbers: T(0,0) = 1, T(n,0) = 0 for n>0; T(n,k) = 0 if k<n; T(n,k)=T(n,k-1)+T(n-1,k-1)+T(n-1,k).
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1
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1, 0, 1, 0, 1, 2, 0, 1, 4, 6, 0, 1, 6, 16, 22, 0, 1, 8, 30, 68, 90, 0, 1, 10, 48, 146, 304, 394, 0, 1, 12, 70, 264, 714, 1412, 1806, 0, 1, 14, 96, 430, 1408, 3534, 6752, 8558, 0, 1, 16, 126, 652, 2490, 7432, 17718, 33028, 41586, 0, 1, 18, 160, 938, 4080, 14002, 39152, 89898, 164512, 206098, 0, 1, 20, 198
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| See A033877 for comments and references etc.
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FORMULA
| G.f.: Sum T(n, k)*x^n*y^k = 1+y*(1-x*y-(x^2*y^2-6*x*y+1)^(1/2))/(2*y+x*y-1+(x^2*y^2-6*x*y+1)^(1/2)).
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EXAMPLE
| 1; 0,1; 0,1,2; 0,1,4,6; 0,1,6,16,22; 0,1,8,30,68,90; ...
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CROSSREFS
| Essentially the same as A033877 except with a leading diagonal 1, 0, 0, 0, ...
Last diagonal: A006318 or A103137; row sums give A001003.
Sequence in context: A139435 A077909 A128749 * A173003 A016584 A112899
Adjacent sequences: A106576 A106577 A106578 * A106580 A106581 A106582
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KEYWORD
| nonn,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 30 2005
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