The On-Line Encyclopedia of Integer Sequences (OEIS)

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A329434

Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*(2*j - 1)))).
(history; published version)

#4 by Susanna Cuyler at Wed Nov 13 15:09:13 EST 2019

STATUS

proposed

approved

#3 by Ilya Gutkovskiy at Wed Nov 13 12:47:32 EST 2019

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Wed Nov 13 11:56:15 EST 2019

NAME

allocated for Ilya Gutkovskiy

Expansion of Sum_{k>=1} (-1 + Product_{j>=1} (1 + x^(k*(2*j - 1)))).

DATA

1, 1, 2, 2, 2, 3, 2, 4, 4, 4, 3, 7, 4, 5, 7, 9, 6, 10, 7, 12, 11, 11, 10, 20, 14, 16, 18, 22, 18, 28, 21, 32, 29, 32, 32, 47, 36, 44, 46, 60, 50, 67, 58, 75, 77, 82, 79, 112, 95, 114, 114, 134, 126, 157, 148, 181, 176, 196, 193, 248, 224, 257, 268, 308, 299

OFFSET

1,3

COMMENTS

Inverse Moebius transform of A000700.

FORMULA

G.f.: Sum_{k>=1} (-1 + Product_{j>=1} 1 / (1 + (-1)^j * x^(k*j))).

G.f.: Sum_{k>=1} A000700(k) * x^k / (1 - x^k).

a(n) = Sum_{d|n} A000700(d).

MATHEMATICA

nmax = 65; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k (2 j - 1))), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest

CROSSREFS

Cf. A000700, A047966, A047968.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Nov 13 2019

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Wed Nov 13 11:56:15 EST 2019

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved