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A025274
a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 5.
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
FORMULA
G.f.: (1-sqrt(1-4x+4x^3+12x^4))/2.
Conjecture: n*a(n) +(n+1)*a(n-1) +10*(-2*n+5)*a(n-2) +2*(2*n-9)*a(n-3) +2*(16*n-91)*a(n-4) +60*(n-7)*a(n-5)=0. - R. J. Mathar, Nov 21 2014
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
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
KEYWORD
nonn,eigen
STATUS
approved