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A203508 G.f.: Product_{n>=0} (1+a(n)*x^(n+1))^3 = Sum_{n>=0} a(n)*x^n. 1
1, 3, 12, 64, 354, 2160, 13518, 88374, 584409, 3980736, 27291825, 190771995, 1339606882, 9539905173, 68140709607, 492072701284, 3560322659379, 25984705308156, 189940383845883, 1398103463338725, 10302144982761213, 76363018655732307, 566463003067056519 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
EXAMPLE
G.f.: A(x) = 1 + 3*x + 12*x^2 + 64*x^3 + 354*x^4 + 2160*x^5 + 13518*x^6 +...
where
A(x) = ((1+x)*(1+3*x^2)*(1+12*x^3)*(1+64*x^4)*(1+354*x^5)*...)^3.
Related expansion:
A(x)^(1/3) = 1 + x + 3*x^2 + 15*x^3 + 76*x^4 + 454*x^5 + 2742*x^6 +...
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))^3, 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[k] x^(k+1))^3, {k, 0, n-1}], {x, 0, n}];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 20 2020 *)
PROG
(PARI) {a(n) = polcoeff(prod(k=0, n-1, (1+a(k)*x^(k+1)+x*O(x^n)))^3, n)}
CROSSREFS
Sequence in context: A124562 A172450 A276743 * A052757 A345883 A365122
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 02 2012
STATUS
approved

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Last modified March 2 18:50 EST 2024. Contains 370498 sequences. (Running on oeis4.)