|
|
A104530
|
|
Expansion of (1+sqrt(1-4x))/(4sqrt(1-4x)-2).
|
|
2
|
|
|
1, 3, 15, 78, 411, 2178, 11574, 61596, 328083, 1748346, 9319650, 49688004, 264943902, 1412826132, 7534329804, 40180417848, 214285867011, 1142822599722, 6094924220394, 32505784870068, 173362418710506, 924593002335612, 4931138212856244, 26299312319336328, 140262655976846766
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Apply the Riordan matrix ((1+sqrt(1-4x))/2,(1-sqrt(1-4x))/2) (inverse of (1/(1-x),x(1-x))) to 4^n.
|
|
LINKS
|
|
|
FORMULA
|
a(n)=0^n+sum{k=0..n, 3^(k+1)*C(2n-1, n-k-1)*2*(k+1)/(n+k+1);
Recurrence: 3*n*a(n) = 2*(14*n-9)*a(n-1) - 32*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 17 2012
|
|
MATHEMATICA
|
CoefficientList[Series[(1+Sqrt[1-4*x])/(4*Sqrt[1-4*x]-2), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 17 2012 *)
|
|
PROG
|
(PARI) x='x+O('x^66); Vec((1+sqrt(1-4*x))/(4*sqrt(1-4*x)-2)) \\ Joerg Arndt, May 13 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|