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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A177043 Central MacMahon numbers: a(n)=A060187(2*n+1, n+1). 3
 1, 6, 230, 23548, 4675014, 1527092468, 743288515164, 504541774904760, 455522635895576646, 527896878148304296900, 763820398700983273655796, 1349622683586635111555174216, 2859794140516672651686471055900, 7157996663278223282076538528360968 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Robert Israel, Table of n, a(n) for n = 0..201 FORMULA a(n) ~ sqrt(3) * 2^(4*n+1) * n^(2*n) / exp(2*n). - Vaclav Kotesovec, Sep 30 2014 MAPLE a:= n-> add((-1)^(n-i) *binomial(2*n+1, n-i) *(2*i+1)^(2*n), i=0..n): seq(a(n), n=0..20); # Alois P. Heinz, Dec 05 2011 # With the generating function of the generalized Eulerian polynomials: gf := proc(n, k) local f; f := (x, t) -> x*exp(t*x/k)/(1-x*exp(t*x)); series(f(x, t), t, n+2); ((1-x)/x)^(n+1)*k^n*n!*coeff(%, t, n): collect(simplify(%), x) end: seq(coeff(gf(2*n, 2), x, n), n=0..13); # Peter Luschny, May 02 2013 MATHEMATICA (*A060187*) p[x_, n_]=(1-x)^(n+1)*Sum[(2*k+1)^n*x^k, {k, 0, Infinity}]; f[n_, m_]:=CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m+1]]; a=Table[f[2*n, n], {n, 0, 20}] CROSSREFS Cf. A000108, A060187, A154420. Sequence in context: A084070 A282736 A277293 * A309009 A117064 A112001 Adjacent sequences: A177040 A177041 A177042 * A177044 A177045 A177046 KEYWORD nonn AUTHOR Roger L. Bagula, May 01 2010 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 8 11:43 EST 2022. Contains 358693 sequences. (Running on oeis4.)