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A210672 a(0)=1; thereafter a(n) = 2*Sum_{k=1..n} binomial(2n,2k)*a(n-k). 7
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.

Exp( Sum_{n >= 1} a(n)*x^n/n) is the o.g.f. for A255929. - Peter Bala, Mar 13 2015

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

Table of n, a(n) for n=0..15.

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

E.g.f.: 1/(3-2*cosh(x)) (even coefficients). - Vaclav Kotesovec, Mar 14 2015

a(n) = Sum_{k = 0..2*n} A163626(2*n,k)*A000045(n+1). - Philippe Deléham, May 25 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

Cf.  A028296, A094088, A210657, A210674, A210676, A255929.

Sequence in context: A156212 A138524 A059516 * A173103 A002704 A015215

Adjacent sequences:  A210669 A210670 A210671 * A210673 A210674 A210675

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 28 2012

STATUS

approved

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Last modified December 3 20:40 EST 2016. Contains 278745 sequences.