|
|
A008789
|
|
a(n) = n^(n+3).
|
|
11
|
|
|
0, 1, 32, 729, 16384, 390625, 10077696, 282475249, 8589934592, 282429536481, 10000000000000, 379749833583241, 15407021574586368, 665416609183179841, 30491346729331195904, 1477891880035400390625, 75557863725914323419136
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.(x): T*(1 +8*T +6*T^2)*(1-T)^(-7); where T=T(x) is Euler's tree function (see A000169). - Len Smiley, Nov 19 2001
E.g.f.: d^3/dx^3 {x^3/(T(x)^3*(1-T(x))}, where T(x) = Sum_{n >= 1} n^(n-1)*x^n/n! is the tree function of A000169. - Peter Bala, Aug 05 2012
|
|
MAPLE
|
printlevel := -1; a := [0]; T := x->-LambertW(-x); f := series((T(x)*(1+8*T(x)+6*(T(x))^2)/(1-T(x))^7), x, 24); for m from 1 to 23 do a := [op(a), op(2*m-1, f)*m! ] od; print(a); # Len Smiley, Nov 19 2001
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008788, A008790, A008791.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|