0,3

In general, if A^n = BINOMIAL(A^(n-1)), then for all integer m>0 there exists an integer sequence B such that B^d = BINOMIAL(A^m) where d=gcd(m+1,n). Also, coefficients of A(k*x)^n = k-th binomial transform of coefficients in A(k*x)^(n-1) for all k>0.

G.f. satisfies: A(x)^6 = A(x/(1-x))^5/(1-x).

A^6 = BINOMIAL(A090362), since A090362=A^5. Also,

BINOMIAL(A) = A090359^2 since 2=gcd(1+1,6),

BINOMIAL(A^2) = A090360^3 since 3=gcd(2+1,6), and

BINOMIAL(A^3) = A090361^2 since 2=gcd(3+1,6).

(PARI) {a(n)=local(A); if(n<1, 0, A=1+x+x*O(x^n); for(k=1, n, B=subst(A^5, x, x/(1-x))/(1-x)+x*O(x^n); A=A-A^6+B); polcoeff(A, n, x))}

Cf. A084784, A090353, A090356, A090359, A090360, A090361, A090362.

Sequence in context: A133306 A128319 A008548 this_sequence A112942 A113390 A122020

Adjacent sequences: A090355 A090356 A090357 this_sequence A090359 A090360 A090361

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Nov 26 2003