Let M and K be given positive integers.

I struggle with how to write efficiently this formula in Maple,mainly because it sums over *pairs* of integers K1 and K2, with the given property that "K1+2*K2=K":

0<=K1<=K,

0<=K2<=K/2

sum { M!/(M-K1-K2)! * K!/(K1! * K2)! * 1/M^K * 1/2^K2 : such that K1 + 2*K2 = K}

The "!" means factorial.

Why the command

coeff(sum(x^i,i=0..999)^500,x,2) prints

Error, unable to compute coeff??

I believe, that memory/cpu issues are not a relevant answer here.

Already

coeff(sum(x^i,i=0..998)^500,x,2) gives the correct result.

Even

coeff(sum(x^i,i=0..998)^500,x,200) is ok.

How do I compute coeffs of longer sums?Or why this limitation is imposed by Maple Server?

How do I set from Maple GUI how much memory from my 4GB RAM and how much CPU time can Maple use before it is shut down?Thank you Jan

How do I solve this in Maple:

M(k,n)=M(k,n-1)+M(k-1,n-1)+M(k-2,n-2) and

M(k,1)=1 and M(1,n)=n

?

Thank you, Jan