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A063023 Reversion of y - y^2 - y^4 - y^5. 3
0, 1, 1, 2, 6, 21, 77, 292, 1143, 4592, 18821, 78364, 330512, 1409149, 6063526, 26298592, 114849110, 504595293, 2228824203, 9891723114, 44087704836, 197255893945, 885630834120, 3988872011820, 18017892014655 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
a(n) = sum(k=0..n-1, (sum(j=floor((n-k-1)/3)..floor((n-k-1)/2), binomial(j,n-k-2*j-1)*binomial(k,j)))*binomial(n+k-1,n-1))/n, n>0, a(0)=0. - Vladimir Kruchinin, May 26 2011
D-finite with recurrence 500*n*(n-1)*(n-2)*(n-3)*(2749734646741*n -12465511712206)*a(n) -4350*(n-1)*(n-2)*(n-3)*(1671932639004*n^2 -9463993359665*n +8542758180998)*a(n-1) +6*(n-2)*(n-3)*(920566361953318*n^3 -5234275380165135*n^2 +1599947907526062*n + 14550951937253720)*a(n-2) -58*(n-3)*(141125952976394*n^4 -1372074713192783*n^3 +3865929553111591*n^2 -1368848933612182*n -5017756051156800)*a(n-3) +3*(-5087969954630151*n^5 +92718860230184360*n^4 -673277365411431865*n^3 +2437688480550464340*n^2 -4405429911017929324*n +3182000337895328880)*a(n-4) -145*(5*n-22)*(5*n-23)*(5*n-26)*(48367137647*n -140254765035)*(5*n-24)*a(n-5)=0. - R. J. Mathar, Mar 21 2022
MAPLE
with(gfun):
F:= RootOf(y-y^2-y^4-y^5-x, y):
DE:=holexprtodiffeq(F, g(x)):
Rec:= diffeqtorec(DE, g(x), a(n)):
f:= rectoproc(Rec, a(n), remember):
map(f, [$0..50]); # Robert Israel, Jan 08 2019
MATHEMATICA
CoefficientList[InverseSeries[Series[y - y^2 - y^4 - y^5, {y, 0, 30}], x], x]
PROG
(Maxima)
a(n):=sum((sum(binomial(j, n-k-2*j-1)*binomial(k, j), j, floor((n-k-1)/3), floor((n-k-1)/2)))*binomial(n+k-1, n-1), k, 0, n-1)/n; /* Vladimir Kruchinin, May 26 2011 */
(Sage) # uses[Reversion from A063022]
Reversion(x - x^2 - x^4 - x^5, 25) # Peter Luschny, Jan 08 2019
(PARI) concat(0, Vec(serreverse(x - x^2 - x^4 - x^5 + O(x^30)))) \\ Michel Marcus, Jan 08 2019
CROSSREFS
Sequence in context: A279561 A360150 A294048 * A150188 A150189 A144169
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Jul 05 2001
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)