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Search: id:A114188
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| A114188 |
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Riordan array (1/(1-x),x(1+x)/(1-x)^2). |
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+0
3
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| 1, 1, 1, 1, 4, 1, 1, 9, 7, 1, 1, 16, 26, 10, 1, 1, 25, 70, 52, 13, 1, 1, 36, 155, 190, 87, 16, 1, 1, 49, 301, 553, 403, 131, 19, 1, 1, 64, 532, 1372, 1462, 736, 184, 22, 1, 1, 81, 876, 3024, 4446, 3206, 1216, 246, 25, 1, 1, 100, 1365, 6084, 11826, 11584, 6190, 1870, 317
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Product of A007318 and A113953, that is, (1/(1-x),x/(1-x))*(1,x(1+2x)). Row sums are A025192. Diagonal sums are A052980. Inverse is A114189. A signed version is A110511.
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FORMULA
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T(n, k)=sum{j=0..n, C(n, j)C(k, j-k)2^(j-k)}; T(n, k)=sum{j=0..n-k, C(k, j)C(n+k-j, 2k)}.
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EXAMPLE
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Triangle begins
1;
1, 1;
1, 4, 1;
1, 9, 7, 1;
1, 16, 26, 10, 1;
1, 25, 70, 52, 13, 1;
1, 36,155,190, 87, 16, 1;
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CROSSREFS
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Sequence in context: A128137 A136100 A141905 this_sequence A110511 A082950 A060102
Adjacent sequences: A114185 A114186 A114187 this_sequence A114189 A114190 A114191
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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), Nov 16 2005
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