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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A366046 Expansion of (1/x) * Series_Reversion( x*(1-x+x^5) ). 2
 1, 1, 2, 5, 14, 41, 124, 384, 1210, 3861, 12434, 40313, 131332, 429250, 1405696, 4606898, 15093714, 49386035, 161204470, 524361475, 1697564726, 5461804480, 17433977340, 55085418075, 171777442668, 526480895241, 1576234101044, 4565064570082, 12573573588000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(32) is negative. LINKS Table of n, a(n) for n=0..28. FORMULA a(n) = (1/(n+1)) * Sum_{k=0..floor(n/5)} (-1)^k * binomial(n+k,k) * binomial(2*n-4*k,n-5*k). D-finite with recurrence +2869*n*(n-1)*(n-2)*(n-3) *(1677311589006610608643886320559970*n -7901147144447740888530692468785127)*(n+1)*a(n) +n*(n-1)*(n-2)*(n-3) *(4812206948859965836199309853686553930*n^2 -175013553719393167658676882522877604813*n +722425524622711754521906472526821274049)*a(n-1) -6*(n-1)*(n-2)*(n-3)*(38041469564276713074625931629796582292*n^3 -434187019812974222921305047255132800148*n^2 +1511627766181757985191668395762224462787*n -1439281919744399515865257001890323358373)*a(n-2) +24*(n-2)*(n-3)*(23107055333611559369905978901014910472*n^4 -291637186969535206075427515674585653736*n^3 +1307639647775331737625407609014469136258*n^2 -2417805672147912309219658141920321176114*n +1512007871663508796078252300169686470055)*a(n-3) -1440*(n-3)*(84804544319929041737751787189252800*n^5 -1067895117008250068418057111395610000*n^4 +3937834774286868181364955550730022660*n^3 +975312620367454094109649406073471780*n^2 -32021390554042442142065879328318104181*n +47001806684644394483446146792519879754)*a(n-4) +72*(755178462485403935795686391926983696*n^6 -9721973068673624889003370906133735808*n^5 +28265101220259707812286453812712428560*n^4 +142279853462074595032386388289908608780*n^3 -1109234048552890437383368746114907399821*n^2 +2608361246800778163937859213150591740973*n -2164380627302236226723222549578816128130)*a(n-5) +48600*(6*n-31)*(3*n-13)*(759087266352800004971495991151992*n^4 -9778945772952612092782558107378828*n^3 +46005785870710778199033560834476886*n^2 -93708439282239876819273711147715309*n +69918682390077087204827334331319595)*a(n-6) +139968*(6*n-37)*(3*n-16)*(2*n-11)*(888737373518089148784593470818*n -3184979270877227150713537195033)*(3*n-14)*(6*n-29)*a(n-7)=0. # R. J. Mathar, Dec 04 2023 MAPLE A366046 := proc(n) add((-1)^k * binomial(n+k, k) * binomial(2*n-4*k, n-5*k), k=0..floor(n/5)) ; %/(n+1) ; end proc: seq(A366046(n), n=0..70) ; # R. J. Mathar, Dec 04 2023 PROG (PARI) a(n) = sum(k=0, n\5, (-1)^k*binomial(n+k, k)*binomial(2*n-4*k, n-5*k))/(n+1); CROSSREFS Cf. A063028, A063033. Cf. A276989, A366024. Sequence in context: A365510 A108626 A365509 * A159772 A161898 A159770 Adjacent sequences: A366043 A366044 A366045 * A366047 A366048 A366049 KEYWORD sign AUTHOR Seiichi Manyama, Sep 27 2023 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 September 8 22:30 EDT 2024. Contains 375759 sequences. (Running on oeis4.)