A117487 - OEIS

A117487

G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5))^2.

1, 2, 5, 10, 20, 36, 63, 104, 169, 264, 405, 604, 888, 1278, 1815, 2536, 3502, 4772, 6437, 8586, 11352, 14866, 19315, 24890, 31851, 40466, 51089, 64092, 79952, 99172, 122386, 150264, 183639, 223394, 270605, 326422, 392225, 469490, 559970, 665542, 788412

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Molien series for S_5 X S_5, cf. A001401.

Molien series for S_k X S_k approaches A000712 as k increases.

Column 5 of table A115994.

Note that a(5) is 20, the scalar product of (1 1 2 3 5) and (5 3 2 1 1 ). a(6) is 36, the scalar product of (1 1 2 3 5 7) and (7 5 3 2 1 1 ).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

MAPLE

# adapted from A115994 kmax := 120 : qmax := kmax/2 : g:=sum(t^k*q^(k^2)/product((1-q^j)^2, j=1..k), k=1..kmax): gser:=series(g, q=0, qmax): for n from 25 to qmax-1 do P :=coeff(gser, q^n) : printf("%a, ", coeff(P, t^5)); od: # R. J. Mathar, Apr 07 2006

MATHEMATICA

CoefficientList[Series[1/(Product[(1-x^j), {j, 5}])^2, {x, 0, 45}], x] (* G. C. Greubel, Jan 01 2020 *)

PROG

(Magma) n:=5; G:=SymmetricGroup(n); H:=DirectProduct(G, G); MolienSeries(H); // N. J. A. Sloane

(PARI) my(x='x+O('x^45)); Vec( 1/(prod(j=1, 5, 1-x^j))^2 ) \\ G. C. Greubel, Jan 01 2020

(Sage)

def A117487_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( 1/(product(1-x^j for j in (1..5)))^2 ).list()

A117487_list(45) # G. C. Greubel, Jan 01 2020

CROSSREFS

Cf. A000027, A000712, A001399, A001400, A006918.