A201959 - OEIS

%I #5 Mar 31 2012 10:23:14

%S 1,2,6,28,200,1686,14322,120856,1046376,10250890,150231950,3231032388,

%T 63012862068,578740591534,-16721732074110,-795532873957712,

%U -563556173628880,1315395887469186834,58144603365684119574,-114890208409408898660,-145164771250945501267380

%N E.g.f. satisfies: A(x*cosh(x)) = x*exp(A(x)).

%F a(n) = n!*T(n,1), T(n,m) = sum(k=1..n-m, T(n-m,k)*m^k/k! - (2^(-m-k+1)*sum(i=0..m+k-1,(m+k-2*i-1)^(n-m-k+1)*binomial(m+k-1,i),i,0,m+k-1))/(n-m-k+1)!*T(k+m-1,m)), n>m, with T(n,n)=1.

%o (Maxima)

%o array(B, 100, 100);

%o fillarray (B, makelist (-1, i, 1, 10000));

%o T(n,m):=if B[n,m]=-1 then B[n,m]:(if n=m then 1 else sum(T(n-m,k)*m^k/k!-(2^(-m-k+1)*sum((m+k-2*i-1)^(n-m-k+1)*binomial(m+k-1,i),i,0,m+k-1))/(n-m-k+1)!*T(k+m-1,m),k,1,n-m)) else B[n,m];

%o makelist(n!*T(n, 1), n, 1, 27);

%K sign

%O 1,2

%A _Vladimir Kruchinin_, Dec 06 2011