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A275255 G.f.: A(x) = x*Product_{n>=1} (1+a(n)^2*x^n) = Sum_{n>=1} a(n)*x^n. 0
1, 1, 1, 2, 5, 30, 930, 865833, 749667649743, 562001585071942995616767, 315845781623376380137718569771289227717728016656 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..11.

FORMULA

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

EXAMPLE

a(1)=a(2)=a(3)=1.

a(4)=a(1)^2*a(2)^2+a(3)^2=2.

a(5)=a(1)^2*a(3)^2+a(4)^2=5.

MATHEMATICA

num = 10; g = Table[1, {n, 1, num}]; g[[1]] = Table[1, {n, 1, num}];

For[i = 2, i <= num, i++, g[[i]] = Table[CoefficientList[Series[Product[(1 + g[[i - 1]][[k]]^2 x^k), {k, 1, num}], {x, 0, num}], x][[n]], {n, 1, num}]; ]; g[[num]]

CROSSREFS

Cf. A032305 for a similar g.f. property.

Sequence in context: A140786 A129951 A127298 * A219273 A000133 A059086

Adjacent sequences:  A275252 A275253 A275254 * A275256 A275257 A275258

KEYWORD

nonn

AUTHOR

Benedict W. J. Irwin, Jul 21 2016

STATUS

approved

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Last modified October 14 17:31 EDT 2019. Contains 328022 sequences. (Running on oeis4.)