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A155997
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Triangle read by rows: t0(n,m)=(Binomial[n, m] + (-1)^m*Binomial[n, m])/2; t(n,m)=t(n,m)+t0(n,n-m).
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0
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2, 1, 1, 2, 0, 2, 1, 3, 3, 1, 2, 0, 12, 0, 2, 1, 5, 10, 10, 5, 1, 2, 0, 30, 0, 30, 0, 2, 1, 7, 21, 35, 35, 21, 7, 1, 2, 0, 56, 0, 140, 0, 56, 0, 2, 1, 9, 36, 84, 126, 126, 84, 36, 9, 1, 2, 0, 90, 0, 420, 0, 420, 0, 90, 0, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Row sums are:
{2, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,...}
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FORMULA
| t0(n,m)=(Binomial[n, m] + (-1)^m*Binomial[n, m])/2;
t(n,m)=t(n,m)+t0(n,n-m).
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EXAMPLE
| {2},
{1, 1},
{2, 0, 2},
{1, 3, 3, 1},
{2, 0, 12, 0, 2},
{1, 5, 10, 10, 5, 1},
{2, 0, 30, 0, 30, 0, 2},
{1, 7, 21, 35, 35, 21, 7, 1},
{2, 0, 56, 0, 140, 0, 56, 0, 2},
{1, 9, 36, 84, 126, 126, 84, 36, 9, 1},
{2, 0, 90, 0, 420, 0, 420, 0, 90, 0, 2}
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MATHEMATICA
| Clear[t, n, m];
t[n_, m_] = (Binomial[n, m] + (-1)^m*Binomial[n, m])/2;
Table[Table[t[n, m] + t[n, n - m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Sequence in context: A194529 A055138 A177717 * A123223 A088226 A117586
Adjacent sequences: A155994 A155995 A155996 * A155998 A155999 A156000
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 01 2009
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