login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323208 a(n) = hypergeometric([-n - 1, n + 2], [-n - 2], n). 3

%I #9 Feb 26 2019 03:58:04

%S 1,5,67,1606,55797,2537781,142648495,9549411950,741894295369,

%T 65620725560578,6511108452179611,716273662860469000,

%U 86527644431076024637,11387523335268377432565,1621766490238904658104583,248507974510512755641561366,40769019250019155227631614225

%N a(n) = hypergeometric([-n - 1, n + 2], [-n - 2], n).

%F a(n) = A323206(n, n+1).

%F a(n) = Sum_{j=0..n+1} (binomial(2*(n+1)-j,n+1)-binomial(2*(n+1)-j,n+2))*n^(n+1-j).

%F a(n) = Sum_{j=0..n+1} binomial(n+1+j, n+1)*(1 - j/(n+2))*n^j.

%F a(n) = 1 + Sum_{j=0..n} ((1+j)*binomial(2*(n+1)-j, n+2)/(n+1-j))*n^(n+1-j).

%F a(n) = (1/(2*Pi))*Integral_{x=0..4*n} (sqrt(x*(4*n-x))*x^(n+1))/(1+(n-1)*x), n>0.

%F a(n) ~ (4^(n + 2)*n^(n + 3))/(sqrt(Pi)*(1 - 2*n)^2*(n + 1)^(3/2)).

%p # The function ballot is defined in A238762.

%p a := n -> add(ballot(2*j, 2*n+2)*n^j, j=0..n+1):

%p seq(a(n), n=0..16);

%t a[n_] := Hypergeometric2F1[-n - 1, n + 2, -n - 2, n];

%t Table[a[n], {n, 0, 16}]

%Y Cf. A323206, A238762.

%K nonn

%O 0,2

%A _Peter Luschny_, Feb 25 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)