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A256665
Triangle of Arnold L(b) for Springer numbers.
1
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
OFFSET
0,6
COMMENTS
Named after Soviet and Russian mathematician Vladimir Igorevich Arnold (1937-2010). - Amiram Eldar, Jun 13 2021
LINKS
Vladimir Igorevich Arnol'd, The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups, Uspekhi Mat. nauk., Vol. 47, No. 1 (1992), pp. 3-45; English version, Russian Math. Surveys, Vol. 47 (1992), pp. 1-51.
FORMULA
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)).
EXAMPLE
0;
1, 1;
0, 1, 2;
11, 11, 10, 8;
0, 11, 22, 32, 40;
361, 361, 350, 328, 296, 256;
MATHEMATICA
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 *)
PROG
(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));
CROSSREFS
Sequence in context: A153521 A153650 A338049 * A086862 A345392 A027828
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Apr 07 2015
STATUS
approved