The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A327731

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A327731

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

#6 by N. J. A. Sloane at Mon Sep 23 15:32:45 EDT 2019

STATUS

proposed

approved

#5 by Andrew Howroyd at Mon Sep 23 14:46:55 EDT 2019

STATUS

editing

proposed

#4 by Andrew Howroyd at Mon Sep 23 14:46:12 EDT 2019

PROG

(PARI) seq(n)={Vec(prod(k=1, n, (1 + x^k + O(x*x^n))^numdiv(k>>valuation(k, 2))))} \\ Andrew Howroyd, Sep 23 2019

STATUS

proposed

editing

#3 by Ilya Gutkovskiy at Mon Sep 23 12:31:41 EDT 2019

STATUS

editing

proposed

#2 by Ilya Gutkovskiy at Mon Sep 23 12:28:59 EDT 2019

NAME

allocated for Ilya Gutkovskiy

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

DATA

1, 1, 1, 3, 3, 5, 8, 10, 14, 21, 28, 36, 51, 65, 86, 117, 148, 190, 251, 316, 402, 519, 647, 814, 1032, 1282, 1593, 1994, 2457, 3029, 3754, 4591, 5617, 6895, 8381, 10193, 12411, 14999, 18125, 21919, 26359, 31672, 38074, 45556, 54468, 65134, 77576, 92322

OFFSET

0,4

COMMENTS

Weigh transform of A001227.

FORMULA

G.f.: Product_{k>=1} (1 + x^k)^A001227(k).

MATHEMATICA

nmax = 47; CoefficientList[Series[Product[(1 + x^k)^DivisorSum[k, Mod[#, 2] &], {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d DivisorSum[d, Mod[#, 2] &], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 47}]

CROSSREFS

Cf. A001227, A107742, A301800, A320650.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Sep 23 2019

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Mon Sep 23 12:28:59 EDT 2019

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved