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 A226703 Triangle read by rows: T(n,k) = binomial(2*n,k)*Stirling2(2*n-k,n). 0
 1, 1, 2, 7, 12, 6, 90, 150, 90, 20, 1701, 2800, 1820, 560, 70, 42525, 69510, 47250, 16800, 3150, 252, 1323652, 2153844, 1506582, 582120, 131670, 16632, 924, 49329280, 80015936, 57093036, 23291268, 5885880, 924924, 84084, 3432, 2141764053, 3466045440, 2509478400, 1063782720, 289429140, 51891840, 6006000, 411840, 12870 (list; table; graph; refs; listen; history; text; internal format)
 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. LINKS FORMULA T(n,k) = binomial(2*n,k)*stirling2(2*n-k,n). T(n,n) = A000984(n). T(n,0) = A007820(n). 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 Cf. A000984, A007820, A129506. Sequence in context: A069748 A064441 A110949 * A126343 A174539 A049409 Adjacent sequences:  A226700 A226701 A226702 * A226704 A226705 A226706 KEYWORD nonn,tabl AUTHOR Vladimir Kruchinin, Jun 15 2013 STATUS approved

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)