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A323208 a(n) = hypergeometric([-n - 1, n + 2], [-n - 2], n). 1
1, 5, 67, 1606, 55797, 2537781, 142648495, 9549411950, 741894295369, 65620725560578, 6511108452179611, 716273662860469000, 86527644431076024637, 11387523335268377432565, 1621766490238904658104583, 248507974510512755641561366, 40769019250019155227631614225 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

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

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).

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

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

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

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

MAPLE

# The function ballot is defined in A238762.

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

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

MATHEMATICA

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

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

CROSSREFS

Cf. A323206, A238762.

Sequence in context: A124435 A123034 A166619 * A262656 A293849 A244589

Adjacent sequences:  A323205 A323206 A323207 * A323209 A323210 A323211

KEYWORD

nonn

AUTHOR

Peter Luschny, Feb 25 2019

STATUS

approved

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Last modified June 28 17:31 EDT 2022. Contains 354907 sequences. (Running on oeis4.)