A163594 a(n+1) equals the coefficient of x^n in the 2^(n-1)-th iteration of g.f. A(x) = Sum_{m>=1} a(m)*x^m for n>=1 with a(1)=1.

1, 1, 2, 20, 804, 108304, 49833296, 87606851264, 641794234287360, 19783636266156204928, 2512584289692759254055168, 1295158553795409705964052724736, 2690610592205668589191756477437574144

Offset: 1

Author

Paul D. Hanna, Aug 10 2009

Keywords

• nonn

Examples

			The coefficients of the 2^(n-1)-th iterations of the g.f. begin:
(1),1,2,20,804,108304,49833296,87606851264,641794234287360,...
1,(2),6,51,1750,222706,100558052,175666197420,1284466715882828,...
1,4,(20),170,4340,474238,204872756,353171251288,2572462315656538,...
1,8,72,(804),15560,1128036,426923128,713954691088,5159170997828364,...
1,16,272,5000,(108304),4271464,962562608,1461234395040,...
1,32,1056,35856,1266720,(49833296),3774562656,3128786120000,...
1,64,4160,273440,18169920,1226585248,(87606851264),12455033590400,...
1,128,16512,2140224,278454400,36359377216,4771446963584,(641794234287360),...
in which the main diagonal forms this sequence shift left.
		

Crossrefs

Cf. A119819.

Programs

PARI

{a(n)=local(F=x+x^2+sum(m=3, n-1, a(m)*x^m), G=x+x*O(x^n)); if(n<1, 0, if(n<=2, 1, for(i=1, n-1, G=subst(F, x, G);F=G); return(polcoeff(G, n-1, x))))}