|
| |
|
|
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
|
Robert Israel, Table of n, a(n) for n = 0..1471
Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012.
Index entries for reversions of series
|
|
|
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
|
|
|
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) # Function Reversion defined in 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
|
Cf. A063019, A063022.
Sequence in context: A242622 A279561 A294048 * A150188 A150189 A144169
Adjacent sequences: A063020 A063021 A063022 * A063024 A063025 A063026
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Olivier Gérard, Jul 05 2001
|
|
|
STATUS
|
approved
|
| |
|
|
