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Search: id:A111505
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| 1, 0, 1, 0, 2, 1, 0, 0, 3, 1, 0, 0, 6, 4, 1, 0, 0, 0, 10, 5, 1, 0, 0, 0, 20, 15, 6, 1, 0, 0, 0, 0, 35, 21, 7, 1, 0, 0, 0, 0, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 126, 84, 36, 9, 1, 0, 0, 0, 0, 0, 252, 210, 120, 45, 10, 1, 0, 0, 0, 0, 0, 0, 462, 330, 165
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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A034869 is the version without zeros.
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FORMULA
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Sum_{n, n>=k} T(n, k) = A001700(k).
Sum_{k =0..2*n} T(2*n, k) = A032443(n).
Sum_{k=0..2*n+1} T(2*n+1, k) = 4^n = A000302(n).
Sum_{k=0..2*n} T(2*n, k)^2 = A036910(n).
Sum_{k=0..2*n+1} T(2*n+1, k)^2 = C(4*n+1, 2*n) = A002458(n) . Paul D. Hanna (pauldhanna(AT)juno.com)
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 2, 1;
0, 0, 3, 1;
0, 0, 6, 4, 1;
0, 0, 0, 10, 5, 1;
0, 0, 0, 20, 15, 6, 1;
0, 0, 0, 0, 35, 21, 7, 1;
0, 0, 0, 0, 70, 56, 28, 8, 1;
0, 0, 0, 0, 0, 126, 84, 36, 9, 1;
0, 0, 0, 0, 0, 252, 210, 120, 45, 10, 1;
0, 0, 0, 0, 0, 0, 462, 330, 165, 55, 11, 1;
0, 0, 0, 0, 0, 0, 924, 792, 495, 220, 66, 12, 1;
0, 0, 0, 0, 0, 0, 0, 1716, 1287, 715, 286, 78, 13, 1;
0, 0, 0, 0, 0, 0, 0, 3432, 3003, 2002, 1001, 364, 91, 14, 1;
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CROSSREFS
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Cf. A007318, A034869, A094527, A111418.
Sequence in context: A105593 A029371 A114374 this_sequence A109264 A130507 A037872
Adjacent sequences: A111502 A111503 A111504 this_sequence A111506 A111507 A111508
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 16 2005
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