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Search: id:A138765
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| A138765 |
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Triangle read by rows, derived from a(n) = N*a(n-1) + a(n-2). |
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+0
1
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| 2, 5, 3, 10, 24, 10, 17, 99, 145, 24, 26, 288, 1090, 840, 65, 37, 675, 5185, 11880, 4901, 168, 50, 1368, 18226, 93024, 129601, 28560, 441, 65, 2499, 51985, 491400, 1669265, 1413720, 166465, 1155, 82, 4224, 127450, 1964024, 13249601, 29953728, 15421330
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Inverse sums of second array terms by rows = 1/1, 1/4, 1/9, 1/16,...; =
Sum__{n=1..inf}{1/a(n)} = Pi^2/6 = 1.6449340668...
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FORMULA
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Triangle read by rows, antidiagonals of a secondary array. The first array = sequences of the form a(n) = N*a(n-1) + a(n-2). N = 1: 1, 1, 2, 3,... N = 2: 1, 2, 5, 12,... N = 3: 1, 3, 10, 33,... .. The second array = (for N = 1,2,3,...) k(1)*k(3), k(2)*k(4), k(3)*k(5),...: 2,....3,....10,.....24,.... 5,...24,...245,....840,... 10,..99,..1090,..11880,... .. The triangle = antidiagonals of the secondary array.
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EXAMPLE
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First few rows of the triangle are:
2;
5, 3;
10, 24, 10;
17, 99, 145, 24;
26, 288, 1090, 840, 65;
37, 675, 5185, 11880, 4901, 168;
50, 1368, 18226, 93024, 129601, 28560, 442;
...
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CROSSREFS
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Sequence in context: A163254 A143121 A101492 this_sequence A097753 A120860 A091809
Adjacent sequences: A138762 A138763 A138764 this_sequence A138766 A138767 A138768
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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), Mar 30 2008
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