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Search: id:A110180
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| A110180 |
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Triangle of generalized central trinomial coefficients. |
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+0
3
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| 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 7, 5, 1, 1, 1, 19, 13, 7, 1, 1, 1, 51, 49, 19, 9, 1, 1, 1, 141, 161, 91, 25, 11, 1, 1, 1, 393, 581, 331, 145, 31, 13, 1, 1, 1, 1107, 2045, 1441, 561, 211, 37, 15, 1, 1, 1, 3139, 7393, 5797, 2841, 851, 289, 43, 17, 1, 1
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Rows sums are A110181. Diagonal sums are A110182. Columns include central trinomial coefficients A002426, A084601, A084603, A084605, A098264. T(n,k)=central coefficient (1+x+kx^2)^n.
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FORMULA
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Number triangle T(n, k)=sum{j=0..floor((n-k)/2), C(n-k, j)C(n-k-j, j)k^j}
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EXAMPLE
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Rows begin
1;
1,1;
1,1,1;
1,3,1,1;
1,7,5,1,1;
1,19,13,7,1,1;
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CROSSREFS
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Sequence in context: A140670 A068845 A081297 this_sequence A005765 A080214 A096066
Adjacent sequences: A110177 A110178 A110179 this_sequence A110181 A110182 A110183
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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 14 2005
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