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
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Apr 07 2015
STATUS
approved