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A025263
a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 4.
0
1, 2, 1, 6, 16, 57, 190, 676, 2418, 8860, 32848, 123413, 468246, 1792700, 6915438, 26856116, 104908160, 411944698, 1625120364, 6437911432, 25600033700, 102145852536, 408840420704, 1641061732941, 6604395207782, 26643368509676
OFFSET
1,2
FORMULA
Recurrence: n*a(n) = 2*(2*n-3)*a(n-1) + 4*(n-3)*a(n-2) - 6*(2*n-9)*a(n-3). - Vaclav Kotesovec, Jan 25 2015
G.f.: 1/2 - sqrt(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; Do[aa[[n]]=Sum[aa[[k]]*aa[[n-k]], {k, 1, n-1}], {n, 4, nmax}]; aa (* Vaclav Kotesovec, Jan 25 2015 *)
CoefficientList[Series[1/2-Sqrt[12x^3-4x^2-4x+1]/2, {x, 0, 50}], x] (* Harvey P. Dale, Jan 01 2022 *)
CROSSREFS
Sequence in context: A068797 A254639 A049951 * A097947 A101032 A366356
KEYWORD
nonn
STATUS
approved