0,2

The n-th row of array A089900 is the n-th binomial transform of the factorials found in row 0: {1!,2!,3!,..,(n+1)!,..}. The hyperbinomial transform of the main diagonal gives: {1,4,27,..,(n+1)^(n+1),..}, which is the next lower diagonal in array A089900.

a(n) = sum_{k=0..n} sum_{i=0..k} (n-k)^(k-i)*binomial(k, i)*(i+1)!

O.g.f.: Sum_{m>=0, n>=1} n!*x^(m+n-1)/(1-m*x)^n - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 18 2003

(PARI) a(n)=if(n<0, 0, sum(k=0, n, sum(i=0, k, (n-k)^(k-i)*binomial(k, i)*(i+1)!)))

(PARI) a(n)=sum(k=0, n, sum(i=0, k, (n-k)^(k-i)*binomial(k, i)*(i+1)!)); (PARI) a(n)=polcoeff(sum(m=0, 2*n, sum(k=1, 2*n, k!*x^(m+k-1)/(1-m*x)^k), x*O(x^n)), n);

Cf. A089900, A089901, A000312.

Sequence in context: A151077 A003703 A136128 this_sequence A093133 A030817 A030845

Adjacent sequences: A089899 A089900 A089901 this_sequence A089903 A089904 A089905

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Nov 14 2003