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A235605
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Shanks's array c_{a,n} (a >= 1, n >= 0) that generalizes Euler and class numbers, read by antidiagonals upwards.
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7
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1, 1, 1, 1, 3, 5, 1, 8, 57, 61, 2, 16, 352, 2763, 1385, 2, 30, 1280, 38528, 250737, 50521, 1, 46, 3522, 249856, 7869952, 36581523, 2702765, 2, 64, 7970, 1066590, 90767360, 2583554048, 7828053417, 199360981, 2, 96, 15872, 3487246, 604935042, 52975108096
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OFFSET
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0,5
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LINKS
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FORMULA
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Shanks gives recurrences.
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EXAMPLE
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The array begins:
A000364: 1, 1, 5, 61, 1385, 50521, 2702765,..
A000281: 1, 3, 57, 2763, 250737, 36581523, 7828053417,..
A000436: 1, 8, 352, 38528, 7869952, 2583554048, 1243925143552,..
A000490: 1,16, 1280, 249856, 90767360, 52975108096, 45344872202240,..
A000187: 2,30, 3522,1066590, 604935042, 551609685150, 737740947722562,..
A000192: 2,46, 7970,3487246, 2849229890, 3741386059246, 7205584123783010,..
A064068: 1,64,15872,9493504,10562158592,18878667833344,49488442978598912,..
...
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MATHEMATICA
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amax = 10; nmax = amax-1; km0 = 10; Clear[cc]; L[a_, s_, km_] := Sum[ JacobiSymbol[-a, 2k+1]/(2k+1)^s, {k, 0, km}]; c[1, n_, km_] := 2(2n)! L[1, 2n+1, km] (2/Pi)^(2n+1) // Round; c[a_ /; a>1, n_, km_] := (2n)! L[a, 2n+1, km] (2a/Pi)^(2n+1)/Sqrt[a] // Round; cc[km_] := cc[km] = Table[ c[a, n, km], {a, 1, amax}, {n, 0, nmax}]; cc[km0]; cc[km = 2km0]; While[ cc[km] != cc[km/2, km = 2km]]; A235605[a_, n_] := cc[km][[a, n+1 ]]; Table[ A235605[ a-n, n], {a, 1, amax}, {n, 0, a-1}] // Flatten (* Jean-François Alcover, Feb 05 2016 *)
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CROSSREFS
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Rows: A000364 (Euler numbers), A000281, A000436, A000490, A000187, A000192, A064068, A064069, A064070, A064071, ...
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KEYWORD
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AUTHOR
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EXTENSIONS
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a(27) removed, a(29)-a(42) added, and typo in name corrected by Lars Blomberg, Sep 10 2015
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STATUS
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approved
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