A201794 E.g.f. satisfies: A(x+1/2*x^2)=x*exp(A(x)).

1, 1, 3, 7, 30, 96, 343, 4117, -7200, -117350, 13210791, -301763373, 352971853, 347188696141, -18233731779780, 353928253113421, 23894270709259005, -2906056754069734431, 143316419628690145837, 1110191131102178184400, -954513349352250528933834, 97402126796076086688319561, -3777060544481584990339497402

Offset

1,3

Links

Table of n, a(n) for n=1..23.

Formula

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

Prog

(Maxima)
array(BB, 100, 100);
fillarray (BB, makelist (-1, i, 1, 1000));
T(n, m):=if BB[n, m]=-1 then BB[n, m]:(if n=m then 1 else sum(T(n-m, k)*m^k/k!-2^(k+m-n-1)*binomial(k+m-1, n-k-m+1)*T(k+m-1, m), k, 1, n-m)) else BB[n, m];
makelist(n!*T(n, 1), n, 1, 27);

Crossrefs

Sequence in context: A227077 A136934 A369083 * A188229 A277739 A098644

Adjacent sequences: A201791 A201792 A201793 * A201795 A201796 A201797

Keyword

sign

Author

Vladimir Kruchinin, Dec 05 2011

Status

approved