Operational recurrences

[N. J. A. Sloane]

There is a very nice paper by Henry Gould in Vol 1 of Fib Quart.
that defines a whole class of recurrences.  I just extracted 
one sequence from the paper, but
many more could be obtained using the same
approach:


%I A001577 M1718 N0681
%S A001577 1,1,2,6,60,2880,2246400,135862272000,10376834265907200000,
%T A001577 77540115374348238323712000000000
%N A001577 An operational recurrence.
%C A001577 Considers recurrences u(n+1) = (d/dx) u_n(x)*u_{n-1}(x) and u(n+1) = x*(d/dx) u_n(x)*u_{n-1}(x). In la
tter, take u_0=1, u_1=x; setting x=1 gives sequence shown here.
%F A001577 Product F_k^F_{n+1-k}, k=1..n.
%D A001577 H. W. Gould, Operational recurrences, Fib. Quart., 1 (No. 1, 1963), 30-33.
%O A001577 1,3
%A A001577 njas
%K A001577 nice,easy,huge,nonn

NJAS