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PROG
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(PARI) /* From definition (requires setting suitable precision) */ \p100
{a(n)=local(A=1+x, X=x+x*O(x^n)); A=suminf(k=0, exp(-1/(1-k*X))/(1-k*X)^k/k!); round(polcoeff(A, n))}
for(n=0, 30, print1(a(n), ", "))
(PARI) /* From a(n) = Sum_{k=1..n} Stirling2(n, k) * C(n+k-1, k-1) */
{Stirling2(n, k) = sum(j=0, k, (-1)^(k+j) * binomial(k, j) * j^n) / k!}
{a(n)=if(n==0, 1, sum(k=1, n, Stirling2(n, k) * binomial(n+k-1, k-1)))}
for(n=0, 30, print1(a(n), ", "))
(PARI) /* As row sums of triangle A245111: */
{A245111(n, k)=local(A=1+x*y); A=sum(k=0, n, 1/(1-k*x+x*O(x^n))^k*y^k/k!*exp(-y/(1-k*x+x*O(x^n))+y*O(y^n))); polcoeff(polcoeff(A, n, x), k, y)}
{a(n) = sum(k=0, n, A245111(n, k))}
/* Print Initial Rows of Triangle A245111: */
{for(n=0, 10, for(k=0, n, print1(A245111(n, k), ", ")); print(""))}
for(n=0, 30, print1(a(n), ", "))
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