A026772 a(n) = T(2n, n-2), T given by A026769.

1, 10, 71, 444, 2616, 14938, 83821, 465654, 2572166, 14164320, 77886902, 428113940, 2353823912, 12950837432, 71326701751, 393289209772, 2171308560036, 12003376308370, 66445540183348, 368304502202306, 2044177115127750

Offset

2,2

Links

G. C. Greubel, Table of n, a(n) for n = 2..500

Formula

Conjecture D-finite with recurrence +n*(683440564498775*n-3571267774541221)*(n+3)*(n+2)*a(n) -(n+2)*(14680943042715007*n^3 -77306402200099276*n^2 -16510019027854595*n +32930242824559728)*a(n-1) +(115576812096278739*n^4 -727966310087371570*n^3 +337449371031094809*n^2 +647464064695228030*n -329302428245597280)*a(n-2) +(-346716352496404327*n^4 +3103154468191226534*n^3 -7064840562647596109*n^2 +5446737046090126798*n -1580651655578866944)*a(n-3) +(-254358906902769779*n^4 +5220327857917926494*n^3 -35539506928992363997*n^2 +87091315541398186522*n -59916163930294990824)*a(n-4) +(4096127756151299723*n^4 -75037442829872206910*n^3 +502301501960009575069*n^2 -1440579074098159574434*n +1469340925940446228608)*a(n-5) +(-9245640254696084879*n^4 +200559435809555913066*n^3 -1613433648622480143829*n^2 +5696178287053438445634*n -7425674215347839990712)*a(n-6) +(7520597900530912203*n^4 -191405326508832207718*n^3 +1814954924843492047041*n^2 -7605473927193409984358*n +11895887009351293007160)*a(n-7) +4*(-461380856200630754*n^4 +13108517874955450215*n^3 -137711835536290769230*n^2 +633868893726787892361*n -1077896915936680091760)*a(n-8) +4*(n-10)*(8653064513346403*n -44432714618958651)*(2*n-13)*(2*n-19)*a(n-9)=0. - R. J. Mathar, Jun 30 2026

Maple

T:= proc(n, k) option remember;
   if n<0 then 0;
   elif k=0 or k=n then 1;
   elif n=2 and k=1 then 2;
   elif k <= (n-1)/2 then
        procname(n-1, k-1)+procname(n-2, k-1)+procname(n-1, k) ;
   else
       procname(n-1, k-1)+procname(n-1, k) ;
   end if ;
end proc;
seq(T(2*n, n-2), n=2..30); # G. C. Greubel, Nov 01 2019

Mathematica

T[n_, k_]:= T[n, k]= If[n<0, 0, If[k==0 || k==n, 1, If[n==2 && k==1, 2, If[k<=(n-1)/2, T[n-1, k-1] + T[n-2, k-1] + T[n-1, k], T[n-1, k-1] + T[n-1, k] ]]]]; Table[T[2*n, n-2], {n, 2, 30}] (* G. C. Greubel, Nov 01 2019 *)

Prog

(SageMath)
@CachedFunction
def T(n, k):
    if (k==0 or k==n): return 1
    elif (n==2 and k==1): return 2
    elif (k<=(n-1)/2): return T(n-1, k-1) + T(n-2, k-1) + T(n-1, k)
    else: return T(n-1, k-1) + T(n-1, k)
[T(2*n, n-2) for n in (2..30)] # G. C. Greubel, Nov 01 2019

Crossrefs

Cf. A026769, A026770, A026771, A026773, A026774, A026775, A026776, A026777, A026778, A026779.

Sequence in context: A215295 A136856 A016218 * A224292 A016098 A129275

Adjacent sequences: A026769 A026770 A026771 * A026773 A026774 A026775

Keyword

nonn,changed

Author

Clark Kimberling

Status

approved