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 A005986 Number of column-strict plane partitions of n. (Formerly M1393) 6
 1, 2, 5, 11, 23, 45, 87, 160, 290, 512, 889, 1514, 2547, 4218, 6909, 11184, 17926, 28449, 44772, 69862, 108205, 166371, 254107, 385617, 581729, 872535, 1301722, 1932006, 2853530, 4194867, 6139361, 8946742, 12984724, 18771092, 27033892 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Note that the asymptotic formula by Gordon and Houten, cited in Stanley's paper (proposition 20.3, p. 274) is for sequence A003293, not for A005986. In addition in the same paper proposition 20.2 is wrong and Wright's formula is incomplete (for correct version see A000219). - Vaclav Kotesovec, Feb 28 2015 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Vaclav Kotesovec, Graph - The asymptotic ratio. Richard P. Stanley, Theory and Application of Plane Partitions, II, Studies in Appl. Math. 50 (1971), 259-279. DOI:10.1002/sapm1971503259. FORMULA G.f.: 1/Product((1-x^i)*Product(1-x^j,j=2*i-1..infinity),i=1..infinity) or 1/Product((1-x^i)^floor((i+3)/2),i=1..infinity). - Vladeta Jovovic, May 21 2006 a(n) ~ Zeta(3)^(25/72) * exp(1/24 - 25*Pi^4 / (3456*Zeta(3)) + 5*Pi^2*n^(1/3) / (24*Zeta(3)^(1/3)) + 3*Zeta(3)^(1/3)*n^(2/3) / 2) / (A^(1/2) * 2^(5/4) * 3^(1/2) * Pi * n^(61/72)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Mar 07 2015 MAPLE with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add(add(d*p(d), d=divisors(j))*b(n-j), j=1..n)/n fi end end: a:=etr(n-> `if`(modp(n, 2)=0, n+2, n+3)/2): seq(a(n), n=0..45);  # Vaclav Kotesovec, Mar 02 2015 after Alois P. Heinz MATHEMATICA CoefficientList[ Series[ Product[1/((1 - x^i)*Product[(1 - x^j), {j, 2 i - 1, 40}]), {i, 40}], {x, 0, 40}], x] (* or *) CoefficientList[ Series[ Product[1/(1 - x^j)^Floor[(j + 3)/2], {j, 40}], {x, 0, 40}], x] (* Robert G. Wilson v, May 12 2014 *) nmax=50; CoefficientList[Series[Product[1/(1-x^k)^((2*k+5-(-1)^k)/4), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 28 2015 *) PROG (PARI) A005986_list(N, x=(O('x^N)+1)*'x)=Vec(prod(k=1, N, 1/(1-x^k)^((k+3)\2))) \\ M. F. Hasler, Sep 26 2018 CROSSREFS Cf. A003293. Sequence in context: A064934 A227637 A171985 * A277828 A147878 A179902 Adjacent sequences:  A005983 A005984 A005985 * A005987 A005988 A005989 KEYWORD nonn AUTHOR EXTENSIONS More terms from Vladeta Jovovic, May 21 2006 STATUS approved

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Last modified October 18 10:39 EDT 2019. Contains 328147 sequences. (Running on oeis4.)