0,3

G.f.: A(x) = 1 + x*B(x)^2; B(x) = 1 + 2*x*C(x)^2; C(x) = 1 + 3*x*D(x)^2; D(x) = 1 + 4*x*E(x)^2; E(x) = 1 + 5*x*F(x)^2; F(x) = 1 + 6*x*G(x)^2; ...

where the respective sequences begin:

A=[1,1,4,28,276,3480,53232,955524,19672320,...];

B=[1,2,12,114,1440,22368,409248,8585088,202733760,...];

C=[1,3,24,288,4440,82080,1752000,42178800,1127335680,...];

D=[1,4,40,580,10560,226560,5532960,150570240,4501422240,...];

E=[1,5,60,1020,21420,523320,14399280,437433780,14479664640,...];

F=[1,6,84,1638,38976,1068480,32716992,1098069504,39896236800,...];

G=[1,7,112,2464,65520,1991808,67189248,2469837888,97765355520,...];

H=[1,8,144,3528,103680,3461760,127569600,5098406400,218459165760,...];

(PARI) {a(n)=local(A=1+(n+1)*x); for(k=0, n, A=1+(n-k+1)*x*A^2 +x*O(x^n)); polcoeff(A, n)}

Cf. A128319.

Sequence in context: A112915 A129683 A081917 this_sequence A032274 A007559 A138208

Adjacent sequences: A128315 A128316 A128317 this_sequence A128319 A128320 A128321

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 07 2007