A117486 Expansion of 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))^2.

1, 2, 5, 10, 20, 34, 59, 94, 149, 224, 334, 480, 685, 950, 1307, 1762, 2357, 3100, 4050, 5220, 6685, 8466, 10659, 13294, 16494, 20298, 24859, 30234, 36609, 44056, 52806, 62952, 74770, 88380, 104112, 122116, 142786, 166304, 193134, 223504, 257954, 296756, 340544

Offset

0,2

Comments

Molien series for S_4 X S_4, cf. A001400.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1,-4,4,4,2,0,-10,0,2,4,4,-4,-1,-2,1,2,-1).

Formula

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

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) - 4*a(n-5) + 4*a(n-6) + 4*a(n-7) + 2*a(n-8) - 10*a(n-10) + 2*a(n-12) + 4*a(n-13) + 4*a(n-14) - 4*a(n-15) - a(n-16) - 2*a(n-17) + a(n-18) + 2*a(n-19) - a(n-20) for n>19. - Colin Barker, Apr 07 2019

Mathematica

CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3)(1-x^4))^2, {x, 0, 50}], x] (* Harvey P. Dale, Jul 22 2012 *)

Prog

(Magma) n:=4; G:=SymmetricGroup(n); H:=DirectProduct(G, G); MolienSeries(H);
(Maxima) a(n):=floor(2*floor(-n/3)*cos(2*%pi*(n+1)/3)/81+(n+2)*cos(%pi*n/ 2)/128+(n+1)*(2835*(n^2+29*n+246)*(-1)^n+6*n^6+414*n^5+11556*n^4 +166944*n^3 +1320045*n^2+5489625*n+10008110)/ 17418240+1/2); /* Tani Akinari, Nov 14 2012 */
(PARI) Vec(1 / ((1 - x)^8*(1 + x)^4*(1 + x^2)^2*(1 + x + x^2)^2) + O(x^40)) \\ Colin Barker, Apr 07 2019

Crossrefs

Column four of table A115994.

Cf. A001400, A001399, A117485, A117487.

Cf. A000027, A006918, A115994.

Sequence in context: A243938 A365630 A126105 * A263002 A325649 A325719

Adjacent sequences: A117483 A117484 A117485 * A117487 A117488 A117489

Keyword

nonn,easy

Author

Alford Arnold, Mar 22 2006

Extensions

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

Status

approved