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!)
A156996 A triangle sequence from polynomial coefficients: p(x,n)=If[n == 0, 1, Sum[Binomial[2*n - m, m]*(n - m)!*(2*n/(2*n - m))*(x - 1)^m, {m, 0, n}]]. 0
-1, 2, 0, 0, 2, 1, 0, 3, 2, 2, 8, 4, 8, 2, 13, 30, 40, 20, 15, 2, 80, 192, 210, 152, 60, 24, 2, 579, 1344, 1477, 994, 469, 140, 35, 2, 4738, 10800, 11672, 7888, 3660, 1232, 280, 48, 2, 43387, 97434, 104256, 70152, 32958, 11268, 2856, 504, 63, 2, 439792, 976000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are:n! ;

{1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600,...}.

These polynomials are hit polynomials for the reduced ménage problem from Riordan.

This first version didn't check with Riordans's table :

I used x^m instead of (x-1)^m.

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, pp. 197-199

LINKS

Table of n, a(n) for n=0..55.

FORMULA

t(n,m) = coefficients(p(x,n)), where p(x,n) = If[n == 0, 1, Sum[Binomial[2*n - m, m]*(n - m)!*(2*n/(2*n - m))*(x - 1)^m, {m, 0, n}]];

EXAMPLE

{1},

{-1, 2},

{0, 0, 2},

{1, 0, 3, 2},

{2, 8, 4, 8, 2},

{13, 30, 40, 20, 15, 2},

{80, 192, 210, 152, 60, 24, 2},

{579, 1344, 1477, 994, 469, 140, 35, 2},

{4738, 10800, 11672, 7888, 3660, 1232, 280, 48, 2},

{43387, 97434, 104256, 70152, 32958, 11268, 2856, 504, 63, 2},

{439792, 976000, 1036050, 695760, 328920, 115056, 30300, 6000, 840, 80, 2},

{4890741, 10749024, 11338855, 7603266, 3614490, 1284360, 349734, 73260, 11649, 1320, 99, 2},

{59216642, 129103992, 135494844, 90758872, 43341822, 15596208, 4351368, 951984, 162558, 21208, 1980, 120, 2}

MATHEMATICA

Table[CoefficientList[If[n == 0, 1, Sum[Binomial[2*n - m, m]*(n - m)!*(2*n/(2*n - m))*(x - 1)^m, {m, 0, n}]], x], {n, 0, 12}]; Flatten[%]

CROSSREFS

Cf. A094314.

Sequence in context: A303906 A178580 A035437 * A029304 A030202 A159818

Adjacent sequences:  A156993 A156994 A156995 * A156997 A156998 A156999

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Feb 20 2009

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 July 2 13:40 EDT 2020. Contains 335401 sequences. (Running on oeis4.)