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A093635 G.f.: A(x) = Product_{n>=0} (1+a(n)*x^(n+1))^2 = Sum_{n>=0} a(n)*x^n. 4
1, 2, 5, 18, 64, 258, 1061, 4572, 19809, 88972, 400600, 1844602, 8511540, 39919338, 187389085, 891158688, 4238242129, 20365627200, 97881057229, 474301930632, 2297986873946, 11213069093460, 54697034675149, 268399278895406 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Equals the self-convolution of A093636.
LINKS
EXAMPLE
( (1+x)(1+2x^2)(1+5x^3)(1+18x^4) )^2 = 1+2x+5x^2+18x^3+...
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 *)
PROG
(PARI) a(n) =polcoeff(prod(i=0, n-1, (1+a(i)*x^(i+1))^2)+x*O(x^n), n)
CROSSREFS
Sequence in context: A148428 A266833 A148429 * A354420 A024025 A360185
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 07 2004
STATUS
approved

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Last modified April 17 11:55 EDT 2024. Contains 371763 sequences. (Running on oeis4.)