A025277 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5, with initial values 0,0,1,1.

0, 0, 1, 1, 0, 1, 2, 1, 2, 6, 6, 7, 20, 30, 34, 75, 140, 182, 322, 644, 972, 1554, 3024, 5091, 8052, 14784, 26378, 43032, 75504, 136994, 232232, 399399, 720356, 1257256, 2161874, 3852576, 6831552, 11858418, 20949304, 37350768

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Programs

Maple

A025277:= gfun:-rectoproc({a(n) = (4 - 24/n)*a(n-4) + (4 - 18/n)*a(n-3), a(1)=0,a(2)=0,a(3)=1,a(4)=1},a(n),remember):
seq(A025277(n),n=1..100); # Robert Israel, Nov 21 2014

Mathematica

nmax = 30; aa = ConstantArray[0,nmax]; aa[[1]] = 0; aa[[2]] = 0; aa[[3]] = 1; aa[[4]] = 1; Do[aa[[n]] = Sum[aa[[k]]*aa[[n-k]],{k,1,n-1}],{n,5,nmax}]; aa (* Vaclav Kotesovec, Jan 25 2015 *)
a[n_] := Sum[Binomial[n-2*m-3, m]*Binomial[2*m+1, n-2*m-3]/(2*m+1), {m, 0, (n-3)/2}]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Apr 03 2015, after Vladimir Kruchinin *)

Maxima

a(n):=sum((binomial(n-2*m-3,m)*binomial(2*m+1,n-2*m-3))/(2*m+1),m,0,(n-3)/2); /* Vladimir Kruchinin, Nov 21 2014 */

Formula

G.f.: -(sqrt(1-4*x^4-4*x^3)-1)/2. - Vladimir Kruchinin, Nov 21 2014

a(n) = sum(m=0..(n-3)/2, (binomial(n-2*m-3,m)*binomial(2*m+1,n-2*m-3))/(2*m+1)). - Vladimir Kruchinin, Nov 21 2014

a(n) = (4 - 24/n)*a(n-4) + (4 - 18/n)*a(n-3). - Robert Israel, Nov 21 2014