A091200 G.f. A(x) satisfies xA(x)^5 = B(xA(x^5)) where B(x) = x/(1-5x).

1, 1, 3, 11, 44, 185, 802, 3553, 15994, 72886, 335387, 1555487, 7261310, 34083382, 160730900, 761039051, 3616102911, 17235223345, 82372594183, 394648349447, 1894921311499, 9116598414141, 43939539520427, 212124129983285

Offset: 0

Author

Paul D. Hanna, Feb 23 2004

Keywords

• nonn

Comments

More generally, given A(x) satisfies xA(x)^p = B(xA(x^p)) where B(x) = x/(1-p*x), then it appears that A(x) is an integer series only when p is prime. This is a special case of sequences with g.f.s that satisfy the more general functional equation xA(x)^m = B(xA(x^m)) originated by Michael Somos; some other examples are A085748, A091188 and A091190.

Crossrefs

Cf. A085748, A091188, A091190.

Programs

PARI

{a(n)=local(A,m); p=5;if(n<0,0,m=1; A=1+O(x); while(m<=n,m*=p; A=x*subst(A,x,x^p); A=(A/(1-p*A)/x)^(1/p));polcoeff(A,n))}