A025279 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5, starting 1,0,-1,1.

1, 0, -1, 1, 2, 5, 8, 13, 20, 38, 86, 215, 526, 1230, 2762, 6115, 13670, 31294, 73258, 173644, 412612, 978074, 2313060, 5472523, 12989654, 30974176, 74174934, 178173000, 428776280, 1033084378, 2491843724, 6018491615, 14559411886, 35279687544

Offset

1,5

Links

Table of n, a(n) for n=1..34.

Formula

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

Recurrence: n*a(n) = 2*(2*n-3)*a(n-1) - 4*(n-3)*a(n-2) - 2*(2*n-9)*a(n-3) + 12*(n-6)*a(n-4). - Vaclav Kotesovec, Jan 25 2015

Maple

A025279 := proc(n)
    option remember ;
    if n < 5 then
        op(n, [1, 0, -1, 1]) ;
    else
        add( procname(i)*procname(n-i), i=1..n-1) ;
    end if;
end proc:
seq(A025279(n), n=1..20) ; # R. J. Mathar, Jan 13 2025

Mathematica

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

Crossrefs

Sequence in context: A076059 A299732 A169952 * A169954 A015724 A290133

Adjacent sequences: A025276 A025277 A025278 * A025280 A025281 A025282

Keyword

sign

Author

Clark Kimberling

Status

approved