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A234324
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Central terms of the triangle of central factorial numbers (A008955).
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5
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1, 5, 273, 44473, 14739153, 8261931405, 7026231453265, 8439654758970225, 13611213226804376865, 28383081191068916580565, 74326386672885754888959569, 238812235698229573137588936105, 923793013650701305781038113833585, 4235104161629281000608041716747118685
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) ~ c * d^n * n!^2 / n^(3/2), where d = 30.472614208903344955058219429421999299236787591960717... and c = 0.27436634881777520262458169083560234658... - Vaclav Kotesovec, Aug 28 2017
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MAPLE
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b:= proc(n, k) option remember; `if`(k=0, 1,
add(b(j-1, k-1)*j^2, j=1..n))
end:
a:= n-> b(2*n, n):
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MATHEMATICA
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Flatten[{1, Table[Coefficient[Expand[Product[1 + k^2*x, {k, 0, 2*n}]], x^n], {n, 1, 15}]}] (* Vaclav Kotesovec, Aug 28 2017 *)
Table[Sum[(-1)^(n-j) * StirlingS1[2*n+1, 2*n+1-j] * StirlingS1[2*n+1, j+1], {j, 0, 2*n}], {n, 0, 15}] (* Vaclav Kotesovec, Aug 28 2017 *)
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PROG
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(Haskell)
a234324 n = a008955 (2 * n) 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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