A122938 - OEIS

A122938

G.f. A(x) satisfies: A(x+x^2) = A(x)^2/(1+x).

1, 1, 1, 2, 6, 27, 160, 1189, 10600, 110161, 1306629, 17408293, 257299241, 4177017722, 73872560359, 1413560616317, 29096001945172, 641010535303531, 15049350893772391, 375084409475304164, 9890697492431533299

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OFFSET

0,4

COMMENTS

Self-convolution equals A122939. See A122888 for the table of self-compositions of x+x^2.

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f.: A(x) = Product_{n>=0} (1 + F_n(x) )^(1/2^(n+1)) where F_0(x)=x, F_{n+1}(x)=F_n(x+x^2); a product that involves the n-th self-compositions of x+x^2.

EXAMPLE

G.f.: A(x) = (1 + x)^(1/2) * (1 + x+x^2)^(1/4) * (1 + x+2x^2+2x^3+x^4)^(1/8) * (1 + x+3x^2+6x^3+9x^4+10x^5+8x^6+4x^7+x^8)^(1/16) *...

PROG

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

CROSSREFS

Cf. A122939 (A^2), A122940 (log), A122941-A122945; A122888 (table).

Sequence in context: A321584 A009308 A032186 * A352139 A234568 A231934

Adjacent sequences: A122935 A122936 A122937 * A122939 A122940 A122941

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 21 2006

STATUS

approved