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A099869
Bisection of A014137.
1
1, 4, 23, 197, 2056, 23714, 290512, 3707852, 48760367, 656043857, 8987427467, 124936258127, 1757900019101, 24987199492705, 358268702159069, 5175497420902741, 75254198337177848, 1100534370899151722, 16176618251666906476, 238861285363295350240
OFFSET
0,2
LINKS
FORMULA
a(n)=sum(binomial(2k, k)/(k+1), k=0..2n). - Emeric Deutsch, Dec 20 2004
Recurrence: n*(2*n+1)*a(n) = 3*(2*n^2+13*n-8)*a(n-1) + 6*(74*n^2 - 305*n + 298)*a(n-2) - 28*(4*n-9)*(4*n-7)*a(n-3). - Vaclav Kotesovec, Oct 17 2012
a(n) ~ 2^(4*n+1/2)/(3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 17 2012
MAPLE
a:=n->sum(binomial(2*k, k)/(k+1), k=0..2*n): seq(a(n), n=0..20); # Emeric Deutsch
MATHEMATICA
Table[Sum[Binomial[2*k, k]/(k+1), {k, 0, 2*n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 17 2012 *)
PROG
(PARI) a(n)=sum(k=0, 2*n, binomial(2*k, k)/(k+1)); \\ Joerg Arndt, May 12 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 19 2004
EXTENSIONS
More terms from Emeric Deutsch, Dec 20 2004
STATUS
approved