A358119 a(n) = Sum_{j=0..n} (-1)^j*binomial(2*n - j, j)*c(n - j)*c(n - j + 2), where c(n) is the n-th Catalan number.

2, 3, 15, 98, 750, 6359, 57939, 556896, 5578764, 57759397, 614328561, 6682078770, 74071710414, 834535805445, 9535609593441, 110306008352832, 1289937458160684, 15231176767392691, 181406519662622559, 2177471166182909994, 26321521760571055830, 320222147815305416123

Offset

0,1

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = 2*(-1)^n*hypergeom([5/2, -n, n + 1], [2, 4], 4).

G.f.: (x+1-(1-14*x+x^2)^(1/2)*hypergeom([-1/2,3/2],[3],-16*x/(1-14*x+x^2)))/(2*x). - Mark van Hoeij, Nov 11 2022

Maple

c := n -> binomial(2*n, n)/(n + 1):
A358119 := n -> add((-1)^j*binomial(2*n-j, j)*c(n-j)*c(n-j+2), j = 0..n):
seq(A358119(n), n = 0 .. 21);

Prog

(Python)
from math import comb
def A358119(n): return sum((-1 if j&1 else 1)*comb((n<<1)-j, j)*comb(n-j<<1, n-j)*comb(n-j+2<<1, n-j+2)//(n-j+1)//(n-j+3) for j in range(n+1)) # Chai Wah Wu, Nov 11 2022

Crossrefs

Cf. A000108, A358118.

Sequence in context: A245107 A177012 A107413 * A238711 A362999 A165657

Adjacent sequences: A358116 A358117 A358118 * A358120 A358121 A358122

Keyword

nonn

Author

Peter Luschny, Nov 11 2022

Status

approved