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Search: id:A116855
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| A116855 |
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Triangle, rows tend to factorial numbers. |
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+0
1
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| 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 6, 4, 1, 1, 2, 6, 13, 5, 1, 1, 2, 6, 24, 23, 6, 1, 1, 2, 6, 24, 67, 36, 7, 1, 1, 2, 6, 24, 120, 146, 52, 8, 1, 1, 2, 6, 24, 120, 411, 272, 71, 9, 1, 1, 2, 6, 24, 120, 720, 1067, 456, 93, 10, 1
(list; table; graph; listen)
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OFFSET
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1,5
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COMMENT
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Difference rows of the triangle columns reoriented into rows create triangle A010027: (1; 1, 1; 1, 2, 3; 1, 3, 9, 11;...)
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FORMULA
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Generate an array by taking binomial transforms of terms in A000255, inverse binomial transform of the factorial numbers (1,1,3,11,53...) as vectors: [1,0,0,0...], [1,1,0,0,0...], [1,1,3,0,0,0,...], [1,1,3,11,0,0,0,...], etc. Antidiagonals of the array become rows of the triangle.
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EXAMPLE
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First few rows of the array are:
1, 1, 1, 1,...
1, 2, 3, 4,...
1, 2, 6, 13,...
1, 2, 6, 24,...
...
First few rows of the triangle are:
1;
1, 1;
1, 2, 1;
1, 2, 3, 1;
1, 2, 6, 4, 1;
1, 2, 6, 13, 5, 1;
1, 2, 6, 24, 23, 6, 1;
1, 2, 6, 24, 67, 36, 7, 1;
...
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CROSSREFS
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Cf. A000255, A010027.
Sequence in context: A047913 A117935 A103462 this_sequence A030111 A096921 A037161
Adjacent sequences: A116852 A116853 A116854 this_sequence A116856 A116857 A116858
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 24 2006
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