A178076 Sequence with a (4,-8) Somos-4 Hankel transform.

1, 0, 2, -2, 8, -20, 64, -200, 656, -2184, 7408, -25456, 88480, -310464, 1098304, -3912896, 14026752, -50557184, 183110400, -666079872, 2432399104, -8914099840, 32772922112, -120844493056, 446793362944, -1656004554752

Offset: 0

Author

Paul Barry, May 19 2010

Keywords

• easy
• sign

Comments

Hankel transform is A178077.

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]*(-2)^(n-2*k-j)*2^k, {j, 0, k}], {k, 0, Floor[n/2]}] + (1 + (-1)^n)/2], {n, 0, 100}] (* 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)*(-2)^(n-2*k-j)*2^k));
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-2k+1))*Sum_{i=0..k} C(k,i)*C(n-k-i-1,n-2k-i)*(-2)^(n-2k-i)*2^i*2^(k-i) ).