|
|
A297200
|
|
Number of label-increasing forests with branching bounded by 4.
|
|
7
|
|
|
1, 1, 1, 2, 6, 24, 119, 703, 4819, 37596, 328871, 3187627, 33907426, 392693219, 4918535904, 66246158633, 954739609059, 14660169150206, 238933675330056, 4119463404086442, 74907534899129351, 1432718565376182929
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
See Riordan 1978 or 1979 for precise definition.
|
|
LINKS
|
|
|
FORMULA
|
E.g.f. F(x) satisfies the ODE: F'(x) = Sum_{j=0..4} (F(x)-1)^j/j! with F(0)=1. - Max Alekseyev, Jul 12 2019
|
|
MAPLE
|
Order := 25; F := rhs( dsolve( { diff(y(x), x) = sum((y(x)-1)^j/j!, j=0..4), y(0)=1 }, y(x), type=series ) ); seq( coeff(F, x, n)*n!, n=0..24 ); # Max Alekseyev, Jul 12 2019
|
|
MATHEMATICA
|
m = 22; F[_] = 0;
Do[F[x_] = 1 + Integrate[Sum[(F[x] - 1)^j/j!, {j, 0, 4}], x] + O[x]^m // Normal, {m}];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|