A025274 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5, starting 1,1,1,0.

1, 1, 1, 0, 2, 5, 14, 42, 122, 360, 1068, 3181, 9526, 28654, 86558, 262528, 799212, 2441538, 7483052, 23004500, 70921492, 219226064, 679328952, 2109948221, 6567539814, 20483936790, 64010196918, 200382350016, 628344541644, 1973428795542

Offset

1,5

Links

Table of n, a(n) for n=1..30.

Formula

G.f.: (1-sqrt(1-4x+4x^3+12x^4))/2.

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

Maple

A025274 := proc(n)
    option remember ;
    if n < 5 then
        op(n, [1, 1, 1, 0]) ;
    else
        add( procname(i)*procname(n-i), i=1..n-1) ;
    end if;
end proc:
seq(A025274(n), n=1..20) ; # R. J. Mathar, Jan 13 2025

Mathematica

nmax = 30; aa = ConstantArray[0, nmax]; aa[[1]] = 1; aa[[2]] = 1; aa[[3]] = 1; aa[[4]] = 0; Do[aa[[n]] = Sum[aa[[k]]*aa[[n-k]], {k, 1, n-1}], {n, 5, nmax}]; aa (* Vaclav Kotesovec, Jan 25 2015 *)
Rest[CoefficientList[Series[(1-Sqrt[1-4x+4x^3+12x^4])/2, {x, 0, 30}], x]] (* Harvey P. Dale, Aug 21 2024 *)

Prog

(PARI) default(seriesprecision, 100); Vec((1-sqrt(1-4*x+4*x^3+12*x^4))/2 + O(x^50)) \\ Michel Marcus, Nov 22 2014

Crossrefs

Sequence in context: A281594 A174176 A298367 * A132833 A293347 A148326

Adjacent sequences: A025271 A025272 A025273 * A025275 A025276 A025277

Keyword

nonn,eigen

Author

Clark Kimberling

Status

approved