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A185951
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Exponential Riordan array (1, x*cosh(x)).
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1
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1, 0, 1, 3, 0, 1, 0, 12, 0, 1, 5, 0, 30, 0, 1, 0, 120, 0, 60, 0, 1, 7, 0, 735, 0, 105, 0, 1, 0, 896, 0, 2800, 0, 168, 0, 1, 9, 0, 15372, 0, 8190, 0, 252, 0, 1, 0, 5760, 0, 114240, 0, 20160, 0, 360, 0, 1, 11, 0, 270765, 0, 556710, 0, 43890, 0, 495, 0, 1, 0, 33792, 0, 4118400, 0, 2084544, 0, 87120, 0, 660, 0, 1
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OFFSET
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1,4
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COMMENTS
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The column k=0 of the array (which contains T(0,0)=1 and otherwise zero) is not included in the triangle.
Also the Bell transform of the sequence "a(n) = n+1 if n is even else 0". For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016
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LINKS
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FORMULA
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T(n,k) = binomial(n,k)/(2^k) * Sum_{i=0..k} binomial(k,i) *(k-2*i)^(n-k), n > k; T(n,n) = 1.
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EXAMPLE
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Array begins
1,
0, 1,
3, 0, 1,
0, 12, 0, 1,
5, 0, 30, 0, 1,
0, 120, 0, 60, 0, 1,
7, 0, 735, 0, 105, 0, 1,
0, 896, 0, 2800, 0, 168, 0, 1,
9, 0, 15372, 0, 8190, 0, 252, 0, 1,
0, 5760, 0, 114240, 0, 20160, 0, 360, 0, 1,
11, 0, 270765, 0, 556710, 0, 43890, 0, 495, 0, 1,
0, 33792, 0, 4118400, 0, 2084544, 0, 87120, 0, 660, 0, 1.
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MAPLE
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if n =k then
1;
else
binomial(n, k)/2^k * add( binomial(k, i)*(k-2*i)^(n-k), i=0..k) ;
end if;
# The function BellMatrix is defined in A264428.
# Adds (1, 0, 0, 0, ..) as column 0.
BellMatrix(n -> `if`(n::even, n+1, 0), 10); # Peter Luschny, Jan 29 2016
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MATHEMATICA
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t[n_, k_] := Binomial[n, k]/(2^k)* Sum[ Binomial[k, i]*(k-2*i)^(n-k), {i, 0, k}]; t[n_, n_] = 1; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 14 2013, from formula *)
BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
B = BellMatrix[Function[n, If[EvenQ[n], n + 1, 0]], rows = 12];
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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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