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A022630 Expansion of Product_{m>=1} (1 + m*q^m)^2. 2
1, 2, 5, 14, 28, 64, 133, 266, 513, 1000, 1873, 3420, 6257, 11078, 19585, 34192, 58714, 99870, 168858, 281666, 467082, 768994, 1253038, 2030658, 3269551, 5227868, 8304467, 13133256, 20630535, 32250274, 50181624, 77653530, 119634925, 183532470, 280245365 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
Self-convolution of A022629. - Alois P. Heinz, Dec 28 2017
G.f.: exp(2*Sum_{j>=1} Sum_{k>=1} (-1)^(j+1)*k^j*x^(j*k)/j). - Ilya Gutkovskiy, Feb 08 2018
MATHEMATICA
nn=34; CoefficientList [Series[ Product[(1 + m*q^m)^2, {m, nn}], {q, 0, nn}], q] (* Robert G. Wilson v, Feb 08 2018 *)
PROG
(PARI) m=50; q='q+O('q^m); Vec(prod(n=1, m, (1+n*q^n)^2)) \\ G. C. Greubel, Feb 16 2018
(Magma) Coefficients(&*[(1+m*x^m)^2:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 16 2018
CROSSREFS
Column k=2 of A297321.
Sequence in context: A349094 A212340 A304719 * A047133 A031874 A120328
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)