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A178080 Sequence with a (1,-1) Somos-4 Hankel transform. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Hankel transform is A178081.
LINKS
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) ).
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 *)
PROG
(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
CROSSREFS
Sequence in context: A068041 A182155 A101586 * A121968 A305329 A161212
KEYWORD
easy,sign
AUTHOR
Paul Barry, May 19 2010
STATUS
approved

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Last modified July 25 01:41 EDT 2024. Contains 374585 sequences. (Running on oeis4.)