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A333180 G.f.: Sum_{k>=1} (k * x^(k^2) * Product_{j=1..k} (1 + x^j)). 4
0, 1, 1, 0, 2, 2, 2, 2, 0, 3, 3, 3, 6, 3, 3, 3, 4, 4, 4, 8, 8, 8, 8, 8, 4, 9, 9, 5, 10, 10, 15, 15, 15, 15, 15, 15, 16, 16, 11, 17, 17, 18, 24, 24, 24, 30, 30, 30, 30, 31, 31, 31, 32, 26, 33, 34, 41, 41, 42, 49, 49, 56, 56, 56, 64, 64, 57, 65, 58, 59, 67, 68 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

FORMULA

a(n) ~ c * A333198^sqrt(n), where c = 0.3836313809149103736315...

Limit_{n->infinity} a(n) / A333181(n) = A060006 = (1/2 + sqrt(23/3)/6)^(1/3) + (1/2 - sqrt(23/3)/6)^(1/3) = 1.32471795724474602596090885...

MATHEMATICA

nmax = 100; CoefficientList[Series[Sum[n*x^(n^2)*Product[1+x^k, {k, 1, n}], {n, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

nmax = 100; p = 1; s = 0; Do[p = Expand[p*(1 + x^k)*x^(2*k - 1)]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += k*p; , {k, 1, Sqrt[nmax]}]; Take[CoefficientList[s, x], nmax + 1]

CROSSREFS

Cf. A268188, A306734, A333181.

Sequence in context: A214664 A214666 A320471 * A127444 A241477 A268243

Adjacent sequences:  A333177 A333178 A333179 * A333181 A333182 A333183

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 10 2020

STATUS

approved

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Last modified May 7 23:48 EDT 2021. Contains 343652 sequences. (Running on oeis4.)