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A362783
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Square array A(n,k) = (n^(2*k + 1) + 1)/(n + 1), n >= 0, k >= 0, read by antidiagonals.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 11, 7, 1, 1, 1, 43, 61, 13, 1, 1, 1, 171, 547, 205, 21, 1, 1, 1, 683, 4921, 3277, 521, 31, 1, 1, 1, 2731, 44287, 52429, 13021, 1111, 43, 1, 1, 1, 10923, 398581, 838861, 325521, 39991, 2101, 57, 1, 1, 1, 43691, 3587227, 13421773, 8138021, 1439671
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OFFSET
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0,9
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LINKS
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FORMULA
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A(n,k) = Sum_{j=0..2*k} (-n)^j.
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EXAMPLE
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Array begins:
=====================================================================
n/k | 0 1 2 3 4 5 6 ...
----+----------------------------------------------------------------
0 | 1 1 1 1 1 1 1 ...
1 | 1 1 1 1 1 1 1 ...
2 | 1 3 11 43 171 683 2731 ...
3 | 1 7 61 547 4921 44287 398581 ...
4 | 1 13 205 3277 52429 838861 13421773 ...
5 | 1 21 521 13021 325521 8138021 203450521 ...
6 | 1 31 1111 39991 1439671 51828151 1865813431 ...
...
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PROG
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(PARI) A(n, k) = (n^(2*k + 1) + 1)/(n + 1) \\ Andrew Howroyd, May 03 2023
(Magma) /* as array */ [[&+[(-n)^j: j in [0..2*k]]: k in [0..6]]: n in [0..6]]; // Juri-Stepan Gerasimov, May 06 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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