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

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.

Cf. A115994, A117485, A117486, A117488, A117489.

Sequence in context: A000710 A160461 A365631 * A263348 A328548 A294536

Adjacent sequences: A117484 A117485 A117486 * A117488 A117489 A117490

Keyword

nonn

Author

Alford Arnold, Mar 22 2006

Extensions

More terms from R. J. Mathar, Apr 07 2006

Entry revised by N. J. A. Sloane, Mar 10 2007

Status

approved