OFFSET
0,3
COMMENTS
Polynomials based on Extended Tepper's Identity
P(n,x)=sum(j=0..n, (-1)^(n-j)*binomial(n,j)*(x+j)^(2*n))/n!.
P(n,x)=sum(j=0..n, binomial(2*n,j)*stirling2(2*n-j,n)*x^j).
P(n,1)=A129506(n).
REFERENCES
G. P. Egorychev. “Integral Representation and the Computation of Combinatorial Sums.” Translations of Mathematical Monographs, Vol. 59, American Mathematical Society, (1984).
F. J. Papp. “Another Proof of Tepper’s Inequality.” Math. Magazine 45 (1972): 119-121.
EXAMPLE
1,
1 +2*x,
7 +12*x +6*x^2,
90 +150*x +90*x^2 +20*x^3,
1701 +2800*x +1820*x^2 +560*x^3 +70*x^4.
MATHEMATICA
Flatten[Table[Binomial[2n, k]StirlingS2[2n-k, n], {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jun 19 2013 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Jun 15 2013
STATUS
approved