A025270 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5.

1, 2, 1, 1, 6, 17, 60, 201, 688, 2370, 8218, 28703, 100846, 356370, 1265918, 4518571, 16200070, 58317298, 210718174, 764015412, 2778955460, 10137598506, 37082361204, 135985402371, 499840932062, 1841260760276, 6796395432602, 25134116857096

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Formula

Conjecture: n*a(n) +2*(-2*n+3)*a(n-1) +4*(-n+3)*a(n-2) +6*(2*n-9)*a(n-3) +20*(n-6)*a(n-4)=0. - R. J. Mathar, Nov 21 2014

G.f.: 1/2 - sqrt(20*x^4+12*x^3-4*x^2-4*x+1)/2. - Vaclav Kotesovec, Jan 25 2015

Mathematica

nmax = 30; aa = ConstantArray[0, nmax]; aa[[1]] = 1; aa[[2]] = 2; 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 *)

Crossrefs

Sequence in context: A123554 A105291 A214631 * A249450 A373343 A331501

Adjacent sequences: A025267 A025268 A025269 * A025271 A025272 A025273

Keyword

nonn

Author

Clark Kimberling

Status

approved