A050147 - OEIS

A050147

a(n) = T(n,n-1), array T as in A050143. Also T(2n+1,n), array T as in A055807.

1, 3, 12, 56, 280, 1452, 7700, 41456, 225648, 1238420, 6840988, 37986984, 211842696, 1185635388, 6655993380, 37463920608, 211350457824, 1194706644516, 6765300359468, 38370431711000, 217931108199672

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

FORMULA

From Vladimir Kruchinin, Nov 25 2014: (Start)

G.f.: x*((-x^2 + 4*x + 1)/(2*sqrt(x^2 - 6*x + 1)) -x/2 + 1/2).

For n >= 2, a(n) = C(2*n-3,n-2) + Sum_{i=0..n-2} C(n,i+1)*C(n+i-2,n-2). (End)

a(n) ~ (1 + sqrt(2))^(2*n-2) / (2^(1/4) * sqrt(Pi*n)). - Vaclav Kotesovec, Feb 14 2021

a(n) = binomial(2*n-3, n-1)*hypergeom([-n+1, -n], [-2*n+3], -1). - Detlef Meya, Dec 04 2023

MATHEMATICA

a[n_]:=Binomial[2*n-3, n-1]*Hypergeometric2F1[-n+1, -n, -2*n+3, -1];

Table[a[n], {n, 1, 21}] (* Detlef Meya, Dec 04 2023 *)

PROG

(Maxima) a(n):=if n=1 then 1 else sum((binomial(n, i+1))*binomial(n+i-2, n-2), i, 0, n-2)+binomial(2*n-3, n-2); /* Vladimir Kruchinin, Nov 25 2014 */

CROSSREFS

Cf. A002003, A006318, A050143, A055807.

Sequence in context: A284843 A107318 A176281 * A259800 A350482 A120921

Adjacent sequences: A050144 A050145 A050146 * A050148 A050149 A050150

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved