|
|
A125280
|
|
Row sums of triangle A125280, which is the convolution triangle of A030266.
|
|
2
|
|
|
1, 2, 5, 15, 53, 217, 1011, 5260, 30041, 185677, 1228209, 8620874, 63792445, 495163451, 4015888557, 33923543492, 297706713081, 2708377382444, 25495655264883, 247952347547483, 2487743315817023, 25717746952124842
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
G.f.: A(x) = (1/x)*G(x)/(1 - G(x)) where G(x) = x + x*G(G(x)) is g.f. of A030266.
|
|
EXAMPLE
|
A(x) = 1 + 2*x + 5*x^2 + 15*x^3 + 53*x^4 + 217*x^5 + 1011*x^6 +...
where 1 - 1/(1 + x*A(x)) = G(x) is the g.f. of A030266:
G(x) = x + x^2 + 2*x^3 + 6*x^4 + 23*x^5 + 104*x^6 + 531*x^7 + 2982*x^8+..
|
|
PROG
|
(PARI) {a(n)=local(G=x+x^2); for(i=0, n, G=x+x*subst(G, x, G+x^2*O(x^n))); polcoeff((-1+1/(1-G))/x, n, x)}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|