0,2

G.f.: A(x) = [(A_0(x) - 1)/x]^(1/2) where A_0(x) = g.f. of A138294.

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.

(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)}

Cf. A138294 (A_0).

Sequence in context: A030826 A030914 A030838 this_sequence A030967 A030858 A030932

Adjacent sequences: A138292 A138293 A138294 this_sequence A138296 A138297 A138298

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 13 2008