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A287318
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Square array A(n,k) = (2*n)! [x^n] BesselI(0, 2*sqrt(x))^k read by antidiagonals.
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8
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1, 1, 0, 1, 2, 0, 1, 4, 6, 0, 1, 6, 36, 20, 0, 1, 8, 90, 400, 70, 0, 1, 10, 168, 1860, 4900, 252, 0, 1, 12, 270, 5120, 44730, 63504, 924, 0, 1, 14, 396, 10900, 190120, 1172556, 853776, 3432, 0, 1, 16, 546, 19920, 551950, 7939008, 32496156, 11778624, 12870, 0
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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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A(n,k) = A287316(n,k) * binomial(2*n,n).
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EXAMPLE
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Arrays start:
k\n| 0 1 2 3 4 5 6
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k=0| 1, 0, 0, 0, 0, 0, 0, ... A000007
k=1| 1, 2, 6, 20, 70, 252, 924, ... A000984
k=2| 1, 4, 36, 400, 4900, 63504, 853776, ... A002894
k=3| 1, 6, 90, 1860, 44730, 1172556, 32496156, ... A002896
k=4| 1, 8, 168, 5120, 190120, 7939008, 357713664, ... A039699
k=5| 1, 10, 270, 10900, 551950, 32232060, 2070891900, ... A287317
k=6| 1, 12, 396, 19920, 1281420, 96807312, 8175770064, ... A356258
k=7| 1, 14, 546, 32900, 2570050, 238935564, 25142196156, ...
k=8| 1, 16, 720, 50560, 4649680, 514031616, 64941883776, ...
k=9| 1, 18, 918, 73620, 7792470, 999283068, 147563170524, ...
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MAPLE
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A287318_row := proc(k, len) local b, ser;
b := k -> BesselI(0, 2*sqrt(x))^k: ser := series(b(k), x, len);
seq((2*i)!*coeff(ser, x, i), i=0..len-1) end:
for k from 0 to 6 do A287318_row(k, 9) od;
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MATHEMATICA
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Table[Table[SeriesCoefficient[BesselI[0, 2 Sqrt[x]]^k, {x, 0, n}] (2 n)!, {n, 0, 6}], {k, 0, 6}]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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