login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..44.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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