A300411 - OEIS

A300411

a(0) = a(1) = 1; a(n) = [x^n] Product_{k=1..n-1} 1/(1 - a(k)*x^a(k)).

1, 1, 1, 4, 9, 14, 19, 24, 45, 75, 105, 135, 229, 359, 503, 647, 1047, 1591, 2272, 2972, 4696, 6996, 9844, 12894, 20064, 29538, 41204, 54407, 84457, 123723, 171757, 225939, 348643, 508693, 703815, 923529, 1423892, 2076942, 2870977, 3763380, 5778379, 8414332, 11621307

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..42.

FORMULA

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

MATHEMATICA

a[n_] := a[n] = SeriesCoefficient[Product[1/(1 - a[k] x^a[k]), {k, 1, n - 1}], {x, 0, n}]; a[0] = a[1] = 1; Table[a[n], {n, 0, 42}]

CROSSREFS

Cf. A006906, A093637, A151945, A196545, A291698, A293806, A293807, A296387.

Sequence in context: A313118 A313119 A293807 * A313120 A313121 A313122

Adjacent sequences: A300408 A300409 A300410 * A300412 A300413 A300414

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 05 2018

STATUS

approved