|
| |
|
|
A272819
|
|
G.f. A(x) satisfies: A( A(x)^2 - A(x)^4 ) = x*A(x) + x*A(x)^2.
|
|
1
|
|
|
|
1, 1, 1, 1, 2, 7, 23, 65, 167, 418, 1078, 2927, 8261, 23677, 67917, 194401, 557097, 1604805, 4655373, 13592002, 39875297, 117379888, 346445156, 1025077295, 3040774879, 9043131251, 26958950829, 80545589421, 241122613367, 723125785251, 2172271809579, 6535785964961, 19693769446456, 59425319779021, 179551868445081, 543187254954865, 1645200904479900
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,5
|
|
|
LINKS
|
|
|
|
FORMULA
|
G.f. A(x) satisfies: A( A(x^2 - x^4) / (x + x^2) ) = x.
|
|
|
EXAMPLE
|
G.f.: A(x) = x + x^2 + x^3 + x^4 + 2*x^5 + 7*x^6 + 23*x^7 + 65*x^8 + 167*x^9 + 418*x^10 + 1078*x^11 + 2927*x^12 +...
where A( A(x)^2 - A(x)^4 ) = x*A(x) + x*A(x)^2.
RELATED SERIES.
A(x)^2 = x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 7*x^6 + 20*x^7 + 65*x^8 + 194*x^9 + 528*x^10 + 1374*x^11 + 3597*x^12 + 9762*x^13 + 27475*x^14 +...
A(x)^4 = x^4 + 4*x^5 + 10*x^6 + 20*x^7 + 39*x^8 + 92*x^9 + 268*x^10 + 824*x^11 + 2431*x^12 + 6824*x^13 + 18720*x^14 + + 51696*x^15 +...
A(x)^2 - A(x)^4 = x^2 + 2*x^3 + 2*x^4 - 3*x^6 + 26*x^8 + 102*x^9 + 260*x^10 + 550*x^11 + 1166*x^12 + 2938*x^13 + 8755*x^14 + 27190*x^15 +...
A(x) + A(x)^2 = x + 2*x^2 + 3*x^3 + 4*x^4 + 6*x^5 + 14*x^6 + 43*x^7 + 130*x^8 + 361*x^9 + 946*x^10 + 2452*x^11 + 6524*x^12 + 18023*x^13 +...
|
|
|
PROG
|
(PARI) {a(n) = my(A=x+x^2); for(i=1, n, A = serreverse( subst(A, x, x^2-x^4 +x^2*O(x^n)) / (x+x^2) ) ); polcoeff(A, n)}
for(n=1, 40, print1(a(n), ", "))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
