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A173611 Self-convolution of A173610. 3
1, 2, 5, 12, 32, 86, 226, 588, 1596, 4372, 12065, 33344, 91344, 249584, 677896, 1836048, 5039672, 13877256, 38405640, 106482832, 296373672, 826270666, 2307068226, 6445895588, 17963996648, 50028938140, 139149397474 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

FORMULA

G.f. satisfies: A(x) = [C(x^2) + x*B(x^2)]^2 where

B(x) = Sum_{n>=0} a(n)^2*x^n = g.f. of A173612 and

C(x) = 1 + Sum_{n>=0} a(n)*a(n+1)*x^(n+1) = g.f. of A173613.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 32*x^4 + 86*x^5 +...

Describe the g.f. of A173612 by:

B(x) = 1 + 4*x + 25*x^2 + 144*x^3 + 1024*x^4 +...+ a(n)^2*x^n +...

and describe the g.f. of A173613 by:

C(x) = 1 + 2*x + 10*x^2 + 60*x^3 + 384*x^4 +...+ a(n)*a(n+1)*x^n +...

then the g.f. of this sequence is given by:

A(x) = [C(x^2) + x*B(x^2)]^2

where A(x) is the square of the g.f. of A173610:

A(x)^(1/2) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 25*x^5 + 60*x^6 +...

PROG

(PARI) {a(n)=local(A=1+x, B); for(i=1, n, B=(A+x*O(x^n))^2; A=1+x*sum(m=0, n\2, polcoeff(B, m)*polcoeff(B, m+1)*x^(2*m+1)) +x*sum(m=0, n\2, polcoeff(B, m)^2*x^(2*m))); polcoeff(A^2, n)}

CROSSREFS

Cf. A173610, A173612, A173613.

Sequence in context: A277863 A039809 A335456 * A292211 A293348 A188287

Adjacent sequences:  A173608 A173609 A173610 * A173612 A173613 A173614

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 22 2010

EXTENSIONS

Edited by Paul D. Hanna, Feb 23 2010

STATUS

approved

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Last modified September 23 04:54 EDT 2020. Contains 337295 sequences. (Running on oeis4.)