|
|
A306152
|
|
Inverse Weigh transform of n^n.
|
|
3
|
|
|
1, 4, 23, 227, 2800, 42599, 763220, 15734615, 366715248, 9533820200, 273549419552, 8586984284469, 292755986184548, 10772849584162694, 425587711650564816, 17966217347001535765, 807152054953801845760, 38451365602113718874568, 1936082850634342992601636
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
(1+x)*(1+x^2)^4*(1+x^3)^23*(1+x^4)^227* ... = 1 + x + 4*x^2 + 27*x^3 + 256*x^4 + ... .
|
|
MAPLE
|
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
end:
a:= n-> n^n-b(n, n-1):
|
|
MATHEMATICA
|
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,
Sum[Binomial[a[i], j]*b[n - i*j, i - 1], {j, 0, n/i}]]];
a[n_] := n^n - b[n, n - 1];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|