|
PROG
|
(PARI) /* E.g.f.: 3/(5 - 4*cosh(x)): */
{a(n) = local(X=x+O(x^(2*n+1))); (2*n)!*polcoeff( 3/(5 - 4*cosh(X)), 2*n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) /* E.g.f.: 1 + Sum_{n>=1} 2*exp(n^2*x)/2^n */
\p100 \\ set precision
{a(n) = round( n!*polcoeff(1+2*sum(m=1, 500, exp(m^2*x +x*O(x^n))/2^m*1.), n))}
for(n=0, 20, print1(a(n), ", "))
(PARI) /* Formula for a(n): */
{Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
{a(n) = if(n==0, 3, sum(k=0, 2*n, 4*k! * Stirling2(2*n, k) ))}
for(n=0, 20, print1(a(n), ", "))
(PARI) /* Formula for a(n): */
{Stirling2(n, k)=n!*polcoeff(((exp(x+x*O(x^n))-1)^k)/k!, n)}
{a(n) = if(n==0, 3, 2*sum(k=1, (2*n+1)\3, (3*k)! * Stirling2(2*n+1, 3*k) / k))}
for(n=0, 20, print1(a(n), ", "))
|