|
|
A210672
|
|
a(0)=1; thereafter a(n) = 2*Sum_{k=1..n} binomial(2n,2k)*a(n-k).
|
|
9
|
|
|
1, 2, 26, 842, 50906, 4946282, 704888186, 138502957322, 35887046307866, 11855682722913962, 4863821092813045946, 2425978759725443056202, 1445750991051368583278426, 1014551931766896667943384042, 828063237870027116855857421306, 777768202388460616924079724057482
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Consider the sequence defined by a(0) = 1; thereafter a(n) = c*Sum_{k = 1..n} binomial(2n,2k)*a(n-k). For c = -3, -2, -1, 1, 2, 3, 4 this is A210676, A210657, A028296, A094088, A210672, A210674, A249939.
The Stirling-Bernoulli transform of Fibonacci(n+1) = 1, 1, 2, 3, 5, 8, 13, ... is 1, 0, 2, 0, 26, 0, 842, 0, 50906, 0, ... - Philippe Deléham, May 25 2015
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ 2*sqrt(Pi/5) * n^(2*n+1/2) / (exp(2*n) * (log((1+sqrt(5))/2))^(2*n+1)). - Vaclav Kotesovec, Mar 13 2015
|
|
MAPLE
|
f:=proc(n, k) option remember; local i;
if n=0 then 1
else k*add(binomial(2*n, 2*i)*f(n-i, k), i=1..floor(n)); fi; end;
g:=k->[seq(f(n, k), n=0..40)];
g(2);
|
|
MATHEMATICA
|
nmax=20; Table[(CoefficientList[Series[1/(3-2*Cosh[x]), {x, 0, 2*nmax}], x] * Range[0, 2*nmax]!)[[2*n+1]], {n, 0, nmax}] (* Vaclav Kotesovec, Mar 14 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|