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A195067
G.f. satisfies: A(x) = Sum{n>=0} x^n * A(2*n*x).
0
1, 1, 3, 17, 191, 4261, 189123, 16723689, 2949213319, 1037964817357, 729449200732395, 1024041038817726353, 2872628913886690237679, 16105674069113302453209781, 180504701103754829110217971731, 4044484405239396750189431682523833
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n-1} 2^k*(n-k)^k * a(k) for n>0 with a(0)=1.
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 + 17*x^3 + 191*x^4 + 4261*x^5 +...
where:
A(x) = 1 + x*A(2*x) + x^2*A(4*x) + x^3*A(6*x) + x^4*A(8*x) + x^5*A(10*x) +...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(k=1, n, A=1+sum(j=1, n, x^j*subst(A, x, 2*j*x))); polcoeff(A, n)}
(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, 2^k*(n-k)^k*a(k)))}
CROSSREFS
Cf. A125282.
Sequence in context: A340881 A163879 A088678 * A158885 A202424 A335343
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 08 2011
STATUS
approved