This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A256665 #20 Mar 01 2025 08:38:36 %S A256665 0,1,1,0,1,2,11,11,10,8,0,11,22,32,40,361,361,350,328,296,256,0,361, %T A256665 722,1072,1400,1696,1952,24611,24611,24250,23528,22456,21056,19360, %U A256665 17408,0,24611,49222,73472,97000,119456,140512,159872,177280 %N A256665 Triangle of Arnold L(b) for Springer numbers. %C A256665 Named after Soviet and Russian mathematician Vladimir Igorevich Arnold (1937-2010). - _Amiram Eldar_, Jun 13 2021 %H A256665 Vladimir Igorevich Arnol'd, <a href="http://mi.mathnet.ru/eng/umn4470">The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups</a>, Uspekhi Mat. nauk., Vol. 47, No. 1 (1992), pp. 3-45; <a href="http://iopscience.iop.org/article/10.1070/RM1992v047n01ABEH000861/pdf">English version</a>, Russian Math. Surveys, Vol. 47 (1992), pp. 1-51. %F A256665 E.g.f.: sinh(x+y)/cosh(2*(x+y))*exp(-y). %F A256665 T(n,m) = abs(Sum_{k=floor((n-m+1)/2)..floor((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)). %e A256665 Triangle begins: %e A256665 0; %e A256665 1, 1; %e A256665 0, 1, 2; %e A256665 11, 11, 10, 8; %e A256665 0, 11, 22, 32, 40; %e A256665 361, 361, 350, 328, 296, 256; %t A256665 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 *) %o A256665 (Maxima) %o A256665 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)); %K A256665 nonn,tabl %O A256665 0,6 %A A256665 _Vladimir Kruchinin_, Apr 07 2015