|
|
A014432
|
|
a(n) = Sum_{i=1..n-1} a(i)*a(n-1-i), with a(0) = 1, a(1) = 3.
|
|
3
|
|
|
1, 3, 3, 12, 30, 111, 363, 1353, 4917, 18777, 71769, 280506, 1103556, 4395009, 17622309, 71220828, 289510662, 1183627137, 4862148753, 20061888924, 83100910530, 345457823493, 1440734205513, 6026408186457, 25275954499905, 106277040064191
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
(n+1)*a(n) = (2*n-1)*a(n-1)+11*(n-2)*a(n-2). - Robert Israel, Sep 10 2020
G.f.: 1 + 3*x/(1 - x - 3*x^2/(1 - x - 3*x^2/(1 - x - 3*x^2/(1 - x - 3*x^2/(1 - ...))))) (continued fraction). - Nikolaos Pantelidis, Nov 24 2022
|
|
MAPLE
|
seq(coeff(convert(series((1+x-sqrt(1-2*x-11*x^2))/(2*x), x, 50), polynom), x, i), i=0..30);
A014431:=proc(n) options remember: local i: if n<2 then RETURN([1, 3][n+1]) else RETURN(add(A014431(i)*A014431(n-1-i), i=1..n-1)) fi:end; seq(A014431(n), n=0..30); # C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004
|
|
MATHEMATICA
|
Rest[CoefficientList[Series[(1+x-Sqrt[1-2x-11x^2])/2, {x, 0, 30}], x]] (* Harvey P. Dale, Apr 17 2019 *)
|
|
PROG
|
(PARI) a(n)=polcoeff((1+x-sqrt(1-2*x-11*x^2+x*O(x^n)))/2, n)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Corrected by C. Ronaldo (aga_new_ac(AT)hotmail.com) and Ralf Stephan, Dec 19 2004
|
|
STATUS
|
approved
|
|
|
|