The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A156995 Triangle T(n, k) = 2*n*binomial(2*n-k, k)*(n-k)!/(2*n-k), with T(0, 0) = 2, read by rows. 5
 2, 1, 2, 2, 4, 2, 6, 12, 9, 2, 24, 48, 40, 16, 2, 120, 240, 210, 100, 25, 2, 720, 1440, 1296, 672, 210, 36, 2, 5040, 10080, 9240, 5040, 1764, 392, 49, 2, 40320, 80640, 74880, 42240, 15840, 4032, 672, 64, 2, 362880, 725760, 680400, 393120, 154440, 42768 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS For n>=1, o.g.f. of n-th row is a polynomial p(x,n) = Sum_{k=0..n} ( 2*n*(n-k)! * binomial(2*n-k, k)/(2*n-k)) * x^k. These polynomials are hit polynomials for the reduced ménage problem (Riordan 1958). REFERENCES J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, pp. 197-199 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n, k) = 2*n*binomial(2*n-k, k)*(n-k)!/(2*n-k), with T(0, 0) = 2. EXAMPLE Triangle starts with: n=0: 2; n=1: 1, 2; n=2: 2, 4, 2; n=3: 6, 12, 9, 2; n=4: 24, 48, 40, 16, 2; n=5: 120, 240, 210, 100, 25, 2; n=6: 720, 1440, 1296, 672, 210, 36, 2; n=7: 5040, 10080, 9240, 5040, 1764, 392, 49, 2; n=8: 40320, 80640, 74880, 42240, 15840, 4032, 672, 64, 2; ... MATHEMATICA T[n_, k_]:= If[n==0, 2, 2*n*Binomial[2*n-k, k]*(n-k)!/(2*n-k)]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, May 14 2021 *) PROG (Magma) A156995:= func< n, k | n eq 0 select 2 else 2*n*Factorial(n-k)*Binomial(2*n-k, k)/(2*n-k) >; [A156995(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, May 14 2021 (Sage) def A156995(n, k): return 2 if (k==n) else 2*n*factorial(n-k)*binomial(2*n-k, k)/(2*n-k) flatten([[A156995(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 14 2021 CROSSREFS Row sums are A300484. Sequence in context: A308302 A225530 A020475 * A131183 A346063 A133770 Adjacent sequences: A156992 A156993 A156994 * A156996 A156997 A156998 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 20 2009 EXTENSIONS Edited and changed T(0,0) = 2 (to make formula continuous and constant along the diagonal k = n) by Max Alekseyev, Mar 06 2018 STATUS approved

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

Last modified December 4 10:52 EST 2023. Contains 367560 sequences. (Running on oeis4.)