A203163 (n-1)-st elementary symmetric function of the first n terms of (1,2,3,4,1,2,3,4,1,2,3,4,...) = A010883.

1, 3, 11, 50, 74, 172, 564, 2400, 2976, 6528, 20736, 86400, 100224, 214272, 670464, 2764800, 3096576, 6524928, 20238336, 82944000, 90906624, 189775872, 585252864, 2388787200, 2579890176, 5350883328, 16434855936, 66886041600

Offset: 1

Author

Clark Kimberling, Dec 30 2011

Keywords

• nonn
• easy

Examples

			Let esf abbreviate "elementary symmetric function". Then
0th esf of {1}:  1;
1st esf of {1,2}:  1+2 = 3;
2nd esf of {1,2,3} is 1*2 + 1*3 + 2*3 = 11.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,48,0,0,0,-576).

Crossrefs

Cf. A010883, A203162, A203164, A203165.

Programs

Mathematica

f[k_] := 1 + Mod[k + 3, 4]; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}]  (* A203163 *)
LinearRecurrence[{0,0,0,48,0,0,0,-576},{1,3,11,50,74,172,564,2400},50] (* Harvey P. Dale, Aug 18 2020 *)

PARI

Vec(x*(36*x^6+28*x^5+26*x^4+50*x^3+11*x^2+3*x+1)/(24*x^4-1)^2 + O(x^100)) \\ Colin Barker, Aug 15 2014

Formula

G.f.: x*(36*x^6 + 28*x^5 + 26*x^4 + 50*x^3 + 11*x^2 + 3*x + 1) / (24*x^4 - 1)^2. - Colin Barker, Aug 15 2014