A201959 E.g.f. satisfies: A(x*cosh(x)) = x*exp(A(x)).

1, 2, 6, 28, 200, 1686, 14322, 120856, 1046376, 10250890, 150231950, 3231032388, 63012862068, 578740591534, -16721732074110, -795532873957712, -563556173628880, 1315395887469186834, 58144603365684119574, -114890208409408898660, -145164771250945501267380

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

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.

Prog

(Maxima)
array(B, 100, 100);
fillarray (B, makelist (-1, i, 1, 10000));
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];
makelist(n!*T(n, 1), n, 1, 27);

Crossrefs

Sequence in context: A356577 A058128 A229112 * A216187 A178446 A324126

Adjacent sequences: A201956 A201957 A201958 * A201960 A201961 A201962

Keyword

sign

Author

Vladimir Kruchinin, Dec 06 2011

Status

approved