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A208898
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A diagonal of rectangular table A208896: a(n) = A208896(n+2,n).
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2
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1, 1, 2, 9, 72, 880, 14946, 331177, 9157984, 305879724, 12036430600, 547226046939, 28298540270928, 1643380366183920, 106042236588594096, 7535372761616117625, 585204851983514095424, 49344635724104556446660, 4491848127809479571999928, 439231681095730953672503448
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OFFSET
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0,3
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COMMENTS
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The g.f. of row n, R(n,x), in the rectangular table A208896 satisfies:
(1) R(n,x) = 1 + x*R(n,x)^n * [d/dx x/R(n,x)] for n>=0.
(2) [x^k] R(n,x)^(k-n+1) = [x^k] R(n,x)^(k-n) for k>=2.
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LINKS
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FORMULA
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a(n) is divisible by n for n>=1.
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EXAMPLE
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a(n)/n = [1,1,3,18,176,2491,47311,1144748,33986636,1203643060,...] for n>=1.
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PROG
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(PARI) {a(n)=local(ROW=1+x+x*O(x^n)); for(i=0, n, ROW=1+x*ROW^(n+2)*deriv(x/ROW)); polcoeff(ROW, n)}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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