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A138295
G.f.: A(x) = (1+x) + x*A_2(x)^2; A_2(x) = (1+x)^2 + x*A_3(x)^2; ...; A_{n}(x) = (1+x)^n + x*A_{n+1}(x)^2 for n>=1 with A(x) = A_1(x).
1
1, 2, 6, 27, 138, 789, 4878, 32114, 222690, 1614412, 12169408, 94991253, 765378476, 6349688936, 54128566708, 473335781532, 4240051400948, 38861053427316, 364044827292880, 3482608706581056, 33995600317705974, 338380105093268866
OFFSET
0,2
FORMULA
G.f.: A(x) = [(A_0(x) - 1)/x]^(1/2) where A_0(x) = g.f. of A138294.
EXAMPLE
G.f.: A(x) = 1 + 2*x + 6*x^2 + 27*x^3 + 138*x^4 + 789*x^5 +...
Given A_{n}(x) = (1+x)^n + x*A_{n+1}(x)^2 for n>=0,
the initial coefficients of the functions A_{n} for n=0..6 are:
A_0 = [1, 1, 4, 16, 78, 420, 2454, 15297, 100660, 694022, ...];
A_1 = [1, 2, 6, 27, 138, 789, 4878, 32114, 222690, 1614412,...];
A_2 = [1, 3, 9, 42, 228, 1377, 8992, 62400, 455252, 3465728,...];
A_3 = [1, 4, 13, 62, 356, 2266, 15586, 113752, 871378, 6953751,...];
A_4 = [1, 5, 18, 88, 531, 3554, 25676, 196609, 1577930, 13174337,...];
A_5 = [1, 6, 24, 121, 763, 5356, 40536, 324882, 2725852, 23763583,...];
A_6 = [1, 7, 31, 162, 1063, 7805, 61731, 516648, 4522200, 41085199,...];
A_0(x) being the g.f. of A138294.
PROG
(PARI) {a(n)=local(A=1); for(i=0, n-1, A=(1+x)^(n-i)+x*(A+x*O(x^n))^2); polcoeff(A, n)}
CROSSREFS
Cf. A138294 (A_0).
Sequence in context: A030826 A030914 A030838 * A030967 A030858 A030932
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 13 2008
STATUS
approved