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

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A243665 Number of 4-packed words of degree n. 8
 1, 1, 71, 35641, 65782211, 323213457781, 3482943541940351, 72319852680213967921, 2637329566270689344838491, 157544683317273333844553610061, 14601235867276343036803577794300631, 2010110081536549910297353731858747088201, 396647963186245408341324212422008625649510771 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See Novelli-Thibon (2014) for precise definition. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..100 (terms n = 0..30 from Peter Luschny) J.-C. Novelli, J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014. See Fig. 16. FORMULA a(n) = (4*n)! * [t^n] 1/(2-g(t^(1/4))) with g(t) = (cos(t) + cosh(t))/2. - Peter Luschny, Jul 07 2015 a(0) = 1; a(n) = Sum_{k=1..n} binomial(4*n,4*k) * a(n-k). - Ilya Gutkovskiy, Jan 21 2020 MAPLE 1/(2-(cos(t^(1/4))+cosh(t^(1/4)))/2): series(%, t, 14): seq((4*n)!*coeff(%, t, n), n=0..12); # Peter Luschny, Jul 07 2015 MATHEMATICA g[t_] := (Cos[t] + Cosh[t])/2; a[n_] := (4n)! SeriesCoefficient[1/(2 - g[t^(1/4)]), {t, 0, n}]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jul 14 2018, after Peter Luschny *) PROG (Sage) # uses[CEN from A243664] A243665 = lambda len: CEN(4, len) A243665(13) # Peter Luschny, Jul 06 2015 (Sage) # Alternatively: def PackedWords4(n):     shapes = ([x*4 for x in p] for p in Partitions(n))     return sum(factorial(len(s))*SetPartitions(sum(s), s).cardinality() for s in shapes) [PackedWords4(n) for n in (0..12)] # Peter Luschny, Aug 02 2015 (PARI) seq(n)={my(a=vector(n+1)); a[1]=1; for(n=1, n, a[1+n]=sum(k=1, n, binomial(4*n, 4*k) * a[1+n-k])); a} \\ Andrew Howroyd, Jan 21 2020 CROSSREFS Cf. A011782, A000670, A094088, A243664, A243665, A243666 for k-packed words of degree n for 0<=k<=5. Sequence in context: A220980 A033527 A112615 * A243686 A131454 A099684 Adjacent sequences:  A243662 A243663 A243664 * A243666 A243667 A243668 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 14 2014 EXTENSIONS a(0)=1 prepended, more terms from Peter Luschny, Jul 06 2015 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.

Last modified November 27 06:40 EST 2020. Contains 338678 sequences. (Running on oeis4.)