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A128899
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Riordan array (1,(1-2x-sqrt(1-4x))/(2x)) .
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1
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1, 0, 1, 0, 2, 1, 0, 5, 4, 1, 0, 14, 14, 6, 1, 0, 42, 48, 27, 8, 1, 0, 132, 165, 110, 44, 10, 1, 0, 429, 572, 429, 208, 65, 12, 1, 0, 1430, 2002, 1638, 910, 350, 90, 14, 1, 0, 4862, 7072, 6188, 3808, 1700, 544, 119, 16, 1, 0, 16796, 15194, 23256, 15504, 7752, 2907, 798
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Let the sequence A(n) = [0/1, 2/1, 1/2, 3/2, 2/3, 4/3, ...] defined by a(2n)=n/(n+1) and a(2n+1)=(n+2)/(n+1) . T(n,k) is the triangle read by rows given by A(n) DELTA A000007 where DELTA is the operator defined in A084938 .
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FORMULA
| T(n,k)=A039598(n-1,k-1) for n>=1, k>=1 ; T(n,0)=0^n . T(n,k)=T(n-1,k-1)+2*T(n-1,k)+T(n-1,k+1) for k>=1, T(n,0)=0^n, T(n,k)=0 if k>n .
T(n,k)+T(n,k+1)=A039599(n,k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 12 2007
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EXAMPLE
| Triangle begins:
1;
0, 1;
0, 2, 1;
0, 5, 4, 1;
0, 14, 14, 6, 1;
0, 42, 48, 27, 8, 1;
0, 132, 165, 110, 44, 10, 1;
0, 429, 572, 429, 208, 65, 12, 1;
0, 1430, 2002, 1638, 910, 350, 90, 14, 1;
0, 4862, 7072, 6188, 3808, 1700, 544, 119, 16, 1;
0, 16796, 15194, 23256, 15504, 7752, 2907, 798, 152, 18, 1 ; ...
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CROSSREFS
| Cf. A000108, A039598.
Sequence in context: A073583 A060136 A088391 * A155887 A113368 A066435
Adjacent sequences: A128896 A128897 A128898 * A128900 A128901 A128902
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 21 2007
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