This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A029863 Expansion of Product_{k >= 1} 1/(1-x^k)^c(k), where c(1), c(2), ... = 2 3 2 3 2 3 2 3 .... 2
 1, 2, 6, 12, 27, 50, 98, 172, 310, 522, 888, 1444, 2357, 3724, 5882, 9072, 13957, 21082, 31732, 47072, 69545, 101540, 147620, 212516, 304631, 433054, 613030, 861616, 1206089, 1677766, 2324844, 3203748, 4398602, 6009390, 8181250 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of partitions of n where there are 2 kinds of odd parts and 3 kinds of even parts. - Ilya Gutkovskiy, Jan 17 2018 LINKS 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. 16. N. J. A. Sloane, Transforms FORMULA Euler transform of period 2 sequence [ 2, 3, ...]. a(n) ~ 5 * exp(sqrt(5*n/3)*Pi) / (48 * n^(3/2)). - Vaclav Kotesovec, Sep 20 2015 EXAMPLE G.f. = 1 + 2*x + 6*x^2 + 12*x^3 + 27*x^4 + 50*x^5 + 98*x^6 + 172*x^7 + ... MATHEMATICA nmax = 50; CoefficientList[Series[Product[1/((1 + x^k)*(1 - x^k)^3), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 20 2015 *) PROG (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( 1 / (eta(x + A)^2 * eta(x^2 + A)), n))}; CROSSREFS Cf. A002513, A085140, A262380. Sequence in context: A327477 A052971 A289443 * A091919 A059078 A166963 Adjacent sequences:  A029860 A029861 A029862 * A029864 A029865 A029866 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 18 18:56 EDT 2019. Contains 328197 sequences. (Running on oeis4.)