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Search: id:A109971
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| 1, 0, 1, 0, 2, 1, 0, 7, 4, 1, 0, 30, 18, 6, 1, 0, 143, 88, 33, 8, 1, 0, 728, 455, 182, 52, 10, 1, 0, 3876, 2448, 1020, 320, 75, 12, 1, 0, 21318, 13566, 5814, 1938, 510, 102, 14, 1, 0, 120175, 76912, 33649, 11704, 3325, 760, 133, 16, 1, 0, 690690, 444015, 197340
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are A001764. Diagonal sums are A109972. Second column is A006013. Third column is A006629.
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FORMULA
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Number triangle T(0, 0)=1, T(0, k)=0, k>0, T(n, k)=(k/n)*binomial(3n-k-1, n-k) otherwise; Riordan array (1, f) where f(1-f)^2=x.
T(n, k)=sum{j=0..n, ((3j+1)/(2n+j+1))(-1)^(j-k)*C(3n, 2n+j)C(j, k)}; - Paul Barry (pbarry(AT)wit.ie), Oct 07 2005
T(n,k)=binomial(3n-k,n-k)*2k/(3n-k). (Paul Barry, May 18 2006)
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EXAMPLE
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Rows begin
1;
0,1;
0,2,1;
0,7,4,1;
0,30,18,6,1;
0,143,88,33,8,1;
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CROSSREFS
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Cf. A092276.
Sequence in context: A111596 A129062 A117651 this_sequence A021896 A075615 A076341
Adjacent sequences: A109968 A109969 A109970 this_sequence A109972 A109973 A109974
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 06 2005
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