0,3

G.f. satisfies: A(x) = 1 + x*sum_{n>=0} x^n*A(x/(1-n*x))/(1-n*x).

From the table (A095788) of iterated binomial transforms of this sequence, the antidiagonal sums form this sequence shift left:

1,1,2,5,14,44,155,605,2584,11956,59461,...

1,2,5,15,51,190,766,3329,15553,77822,...

1,3,10,37,150,656,3059,15111,78840,...

1,4,17,77,371,1892,10154,57077,334993,...

1,5,26,141,798,4708,28891,183953,1212664,...

1,6,37,235,1539,10394,72350,518505,3821409,...

1,7,50,365,2726,20840,163091,1306139,10699288,...

1,8,65,537,4515,38656,337114,2994701,27094705,...

1,9,82,757,7086,67292,648539,6344517,63004248,...

1,10,101,1031,10643,111158,1175006,12573713,...

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

Cf. A095788.

Sequence in context: A118929 A081558 A014322 this_sequence A060996 A134378 A101226

Adjacent sequences: A095145 A095146 A095147 this_sequence A095149 A095150 A095151

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Jun 05 2004