A093635 G.f.: A(x) = Product_{n>=0} (1+a(n)*x^(n+1))^2 = Sum_{n>=0} a(n)*x^n.

1, 2, 5, 18, 64, 258, 1061, 4572, 19809, 88972, 400600, 1844602, 8511540, 39919338, 187389085, 891158688, 4238242129, 20365627200, 97881057229, 474301930632, 2297986873946, 11213069093460, 54697034675149, 268399278895406

Offset: 0

Author

Paul D. Hanna, Apr 07 2004

Keywords

• nonn

Comments

Equals the self-convolution of A093636.

Examples

			( (1+x)(1+2x^2)(1+5x^3)(1+18x^4) )^2 = 1+2x+5x^2+18x^3+...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..450

Crossrefs

Cf. A032305, A093636.

Programs

Maple

A:= proc(n) option remember; local i, p, q; if n=0 then 1 else
      p, q:= A(n-1), 1; for i from 0 to n-1 do q:= convert(
        series(q*(1+coeff(p, x, i)*x^(i+1))^2, x, n+1), polynom)
      od: q fi
    end:
a:= n-> coeff(A(n), x, n):
seq(a(n), n=0..30);  # Alois P. Heinz, Aug 01 2013

Mathematica

a[n_] := a[n] = SeriesCoefficient[Product[(1+a[i]*x^(i+1))^2, {i, 0, n-1}], {x, 0, n}];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 02 2020, after PARI *)

PARI

a(n) =polcoeff(prod(i=0,n-1,(1+a(i)*x^(i+1))^2)+x*O(x^n),n)