A010884 -id:A010884 - cp's OEIS frontend

A203166 (n-1)-st elementary symmetric function of the first n terms of (1,2,3,4,5,1,2,3,4,5,...)=A010884.

1, 3, 11, 50, 274, 394, 908, 2964, 12576, 65760, 80160, 174720, 552960, 2298240, 11836800, 13564800, 28857600, 90028800, 370483200, 1893888000, 2101248000, 4409856000, 13644288000, 55821312000, 284083200000, 308966400000

Offset: 1

Clark Kimberling, Dec 30 2011

nonn

Cf. A010884, A203163.

f[k_] := 1 + Mod[k + 4, 5];
t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[n - 1, t[n]]
Table[a[n], {n, 1, 33}]  (* A203166 *)

Conjecture: G.f. x*(1+3*x+11*x^2+50*x^3+274*x^4+154*x^5+188*x^6+324*x^7+576*x^8) / (-1+120*x^5)^2 with a(n) = 240*a(n-5) -14400*a(n-10). - R. J. Mathar, Jul 02 2013

A177038 Decimal expansion of (195+sqrt(65029))/314.

Original entry on oeis.org

1, 4, 3, 3, 1, 4, 5, 9, 9, 6, 8, 6, 8, 2, 8, 4, 5, 6, 3, 2, 7, 8, 7, 6, 8, 2, 8, 9, 4, 7, 3, 1, 0, 8, 7, 4, 0, 4, 4, 4, 6, 7, 1, 5, 5, 6, 0, 4, 7, 5, 4, 3, 8, 6, 3, 3, 0, 3, 6, 5, 7, 6, 3, 8, 8, 8, 9, 2, 7, 0, 9, 5, 7, 9, 6, 2, 7, 4, 7, 7, 1, 0, 8, 4, 5, 2, 9, 7, 3, 6, 9, 6, 4, 5, 0, 4, 9, 2, 4, 8, 7, 6, 4, 6, 0

Offset: 1

Klaus Brockhaus, May 01 2010

Continued fraction expansion of (195+sqrt(65029))/314 is A010884.

			(195+sqrt(65029))/314 = 1.43314599686828456327...

Cf. A177039 (decimal expansion of sqrt(65029)), A010884 (repeat 1, 2, 3, 4, 5).

RealDigits[(195+Sqrt[65029])/314,10,120][[1]] (* Harvey P. Dale, Nov 29 2023 *)

cp's OEIS Frontend

A203166 (n-1)-st elementary symmetric function of the first n terms of (1,2,3,4,5,1,2,3,4,5,...)=A010884.

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