A178080 Sequence with a (1,-1) Somos-4 Hankel transform.

1, 0, -1, -1, -2, -6, -14, -27, -39, -4, 269, 1415, 5258, 16321, 43705, 98459, 163216, 49326, -1120684, -6502098, -25711856, -83830889, -233926105, -545916369, -932372648, -280663557, 6802456973, 40262637059, 162298734532, 538385811978

Offset: 0

Author

Paul Barry, May 19 2010

Keywords

• easy
• sign

Comments

Hankel transform is A178081.

Links

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

Programs

Mathematica

Table[If[n == 0, 1, Sum[(Binomial[n-k, k]/(n-2*k+1))*Sum[Binomial[k, j]* Binomial[n-k-j-1, n-2*k-j]*3^(n-2*k-j)*2^j*(-1)^(k-j), {j, 0, k}], {k, 0, Floor[n/2]}] + ((1 + (-1)^n)*(-2/3)^(n/2))/2], {n, 0, 50}] (* G. C. Greubel, Sep 18 2018 *)

PARI

a(n) = sum(k=0,floor(n/2), sum(j=0,k, (binomial(n-k,k)/(n-2*k+1)) *binomial(k,j)*binomial(n-k-j-1,n-2*k-j)*3^(n-2*k-j)*2^j*(-1)^(k-j)));
for(n=0,30, print1(a(n), ", ")) \\ G. C. Greubel, Sep 18 2018

Formula

a(n) = Sum_{k=0..floor(n/2)} ( (C(n-k,k)/(n-2*k+1))*Sum_{i=0..k} C(k,i)*C(n-k-i-1,n-2*k-i)*3^(n-2k-i)*2^i*(-1)^(k-i) ).