A324614 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * (1 + n*x)^n / A(x)^(n+1).

1, 1, 1, 2, 3, 9, 21, 76, 241, 962, 3687, 15930, 68993, 320025, 1511977, 7471685, 37780922, 197506241, 1056928087, 5810534182, 32667061545, 187952045908, 1104355482420, 6623724997302, 40514607315969, 252490521215350, 1602602016169781, 10349126940718990, 67984993381548943, 453846136553840921, 3078734565764856380, 21202631838742029002, 148238158399524358952, 1051257411796217414475

Offset: 0

Author

Paul D. Hanna, Mar 19 2019

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 9*x^5 + 21*x^6 + 76*x^7 + 241*x^8 + 962*x^9 + 3687*x^10 + 15930*x^11 + 68993*x^12 + 320025*x^13 + 1511977*x^14 + ...
such that
1 = 1/A(x) + x*(1+x)/A(x)^2 + x^2*(1+2*x)^2/A(x)^3 + x^3*(1+3*x)^3/A(x)^4 + x^4*(1+4*x)^4/A(x)^5 + x^5*(1+5*x)^5/A(x)^6 + x^6*(1+6*x)^6/A(x)^7 + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A303058.

Programs

PARI

{a(n) = my(A=[1]); for(i=1,n, A=concat(A,0);
A[#A] = polcoeff( sum(n=0,#A, x^n*(1+n*x)^n/Ser(A)^(n+1)), #A-1););A[n+1]}
for(n=0,40, print1(a(n),", "))