OFFSET
1,2
FORMULA
a(n)=[x^n] (1+x+x^2+x^3)^n-(1+x+x^2+x^3)^(n-1). - Michael Somos, Jul 19 2002
a(n)*790*(2*n^2-n) = a(n-1)*(-16328*n^4+137200*n^3-400977*n^2+489925*n-207450)+a(n-2)*(44902*n^4-399751*n^3+1267117*n^2-1672482*n+769980)+a(n-3)*4*(n-3)*(8164*n^3-52272*n^2+115397*n-81223)+a(n-4)*16*(n-4)*(n-3)*(4082*n^2-11849*n+8529), n>2. - Michael Somos, Jul 19 2002
a(n) = sum(k=1..n, (sum(j=0..k, binomial(j,n-3*k+2*j) *binomial(k,j))) *binomial(n-1,n-k)). [Vladimir Kruchinin, Nov 07 2013]
PROG
(PARI) a(n)=local(y=(x^4-1)/(x-1)); if(n<0, 0, polcoeff(y^n-y^(n-1), n))
(Maxima) a(n):=sum((sum(binomial(j, n-3*k+2*j)*binomial(k, j), j, 0, k))*binomial(n-1, n-k), k, 1, n); /* Vladimir Kruchinin, Nov 07 2013 */
CROSSREFS
KEYWORD
nonn,base
AUTHOR
John W. Layman, Jun 22 2002
STATUS
approved