OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 8.
Mohammed L. Nadji and Moussa Ahmia, Congruences for L-regular tripartitions for L in {2, 3}, Integers (2024) Vol. 24, Art. No. A86. See p. 2.
FORMULA
a(n) ~ exp(Pi * sqrt(n)) / (8 * n^(3/4)) * (1 + (Pi/16 - 3/(8*Pi)) / sqrt(n)). - Vaclav Kotesovec, Mar 05 2015, extended Jan 16 2017
a(0) = 1, a(n) = (3/n)*Sum_{k=1..n} A000593(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 03 2017
G.f.: exp(3*Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 06 2018
MATHEMATICA
nmax=50; CoefficientList[Series[Product[(1+q^m)^3, {m, 1, nmax}], {q, 0, nmax}], q] (* Vaclav Kotesovec, Mar 05 2015 *)
nmax = 50; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 3; poly[[3]] = 3; poly[[4]] = 1; Do[Do[Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; , {p, 1, 3}], {k, 2, nmax}]; poly (* Vaclav Kotesovec, Mar 31 2018 *)
PROG
(PARI) x='x+O('x^51); Vec(prod(m=1, 50, (1 + x^m)^3)) \\ Indranil Ghosh, Apr 03 2017
(Magma) Coefficients(&*[(1+x^m)^3:m in [1..40]])[1..40] where x is PolynomialRing(Integers()).1; // G. C. Greubel, Feb 26 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved