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Search: id:A116853
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| A116853 |
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Difference triangle of factorial numbers read by upward diagonals. |
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+0
2
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| 1, 1, 2, 3, 4, 6, 11, 14, 18, 24, 53, 64, 78, 96, 120, 309, 362, 426, 504, 600, 720, 2119, 2428, 2790, 3216, 3720, 4320, 5040, 16687, 18806, 21234, 24024, 27240, 30960, 35280, 40320
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Leftmost column of the triangle = A000255, inverse binomial transform of the factorial numbers. First difference row of factorial numbers = A001563, second difference row = A001564, third difference row = A001565, fourth difference row = A001688, fifth difference row = A001689.
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FORMULA
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Take successive difference rows of factorial numbers n! starting with n=1. Reorient into a triangle format.
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EXAMPLE
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Starting with 1, 2, 6, 24, 120...we take the first difference row (A001563), second, third, etc. Reorient into a flush left format, getting:
1;
1, 2;
3, 4, 6;
11, 14, 18, 24;
53, 64, 78, 96, 120;
309, 362, 426, 504, 600;
...
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CROSSREFS
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Cf. A000255, A001563, A001564, A001565, A001688, A001689.
Adjacent sequences: A116850 A116851 A116852 this_sequence A116854 A116855 A116856
Sequence in context: A018297 A050886 A079310 this_sequence A066615 A133951 A111124
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 24 2006
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