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A256665
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Triangle of Arnold L(b) for Springer numbers.
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1
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0, 1, 1, 0, 1, 2, 11, 11, 10, 8, 0, 11, 22, 32, 40, 361, 361, 350, 328, 296, 256, 0, 361, 722, 1072, 1400, 1696, 1952, 24611, 24611, 24250, 23528, 22456, 21056, 19360, 17408, 0, 24611, 49222, 73472, 97000, 119456, 140512, 159872, 177280
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OFFSET
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0,6
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COMMENTS
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Named after Soviet and Russian mathematician Vladimir Igorevich Arnold (1937-2010). - Amiram Eldar, Jun 13 2021
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LINKS
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FORMULA
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E.g.f.: sinh(x+y)/cosh(2*(x+y))*exp(-y).
T(n,m) = abs(Sum_{ k=floor((n-m+1)/2)..(n+1)/2)} C(m,2*k+m-n-1)*Sum_{ i=0..k }4^i*Euler(2*i)*C(2*k-1,2*i)).
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EXAMPLE
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0;
1, 1;
0, 1, 2;
11, 11, 10, 8;
0, 11, 22, 32, 40;
361, 361, 350, 328, 296, 256;
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MATHEMATICA
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T[n_, m_] := Abs[Sum[Binomial[m, 2*k+m-n-1]*Sum[4^i*EulerE[2*i]*Binomial[2*k-1, 2*i], {i, 0, k}], {k, Floor[(n-m+1)/2], (n+1)/2}]]; Table[T[n, m], {n, 0, 10}, {m, 0, n}] // Flatten (* Jean-François Alcover, Apr 07 2015, translated from Maxima *)
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PROG
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(Maxima)
T(n, m):=abs(sum(binomial(m, 2*k+m-n-1)*sum(4^i*euler(2*i)*binomial(2*k-1, 2*i), i, 0, k), k, floor((n-m+1)/2), (n+1)/2));
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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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