A112521 Sequence related to NOR bracketings.

0, 1, 0, 6, 4, 60, 84, 700, 1440, 8910, 23100, 120120, 360360, 1684956, 5552064, 24302520, 85101456, 357502860, 1302562404, 5333981796, 19947127200, 80408748420, 305922388200, 1221485157360, 4701015343440, 18664243014300

Offset

0,4

Comments

Conjecture: Starting with n=1, a(n) is the main diagonal of the array defined as T(1,1) = 1, T(i,j) = 0 if i<1 or j<1, T(n,k) = T(n,k-2) + T(n,k-1) -2*T(n-1,k-1) + T(n-1,k) + T(n-2,k). - Gerald McGarvey, Oct 07 2008

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = Sum_{j=0..n} (-1)^(j-1)*C(2*n-j-1, n-j)*C(2*(j-1), j-1). - corrected by Peter Bala, Aug 19 2014

a(n) = n*A055392(n), n>1.

a(n) = binomial(2*n-2, n-1)*Hypergeometric([-(n-1), 1/2], [2-2*n], -4) with a(0) = 0, a(1) = 1. - G. C. Greubel, Jan 11 2022

Mathematica

a[n_]:= Sum[(-1)^j*Binomial[2*j, j]*Binomial[2*n-j-2, n-j-1], {j, 0, n-1}];
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Jan 11 2022 *)

Prog

(PARI) a(n) = sum(j=0, n, (-1)^(j-1)*binomial(2*n-j-1, n-j)*binomial(2*(j-1), j-1)); \\ Michel Marcus, Aug 19 2014
(Sage)
def a(n): return n if (n<2) else binomial(2*n-2, n-1)*simplify( hypergeometric([-(n-1), 1/2], [2-2*n], -4) )
[a(n) for n in (0..30)] # G. C. Greubel, Jan 11 2022

Crossrefs

Cf. A055392.

Sequence in context: A333813 A327370 A260716 * A192350 A308900 A354949

Adjacent sequences: A112518 A112519 A112520 * A112522 A112523 A112524

Keyword

easy,nonn

Author

Paul Barry, Sep 09 2005

Status

approved