

A203242


Second elementary symmetric function of the first n terms of (1, 3, 7, 15, 31, ...).


2



3, 31, 196, 1002, 4593, 19833, 82818, 339340, 1375639, 5543331, 22263216, 89249214, 357422541, 1430607325, 5724394990, 22901773824, 91616007699, 366482904615, 1465971463740, 5863969740370, 23456055121513, 93824589584001
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OFFSET

2,1


LINKS

Robert Israel, Table of n, a(n) for n = 2..1659


FORMULA

Conjecture: (103*n+258)*a(n) + (881*n2116)*a(n1) + 6*(427*n+960)*a(n2) + 4*(766*n1545)*a(n3) + 16*(80*n+121)*a(n4) = 0.  R. J. Mathar, Oct 15 2013
Empirical g.f.: x^2*(4*x^2 + 2*x  3)/((x  1)^3*(2*x  1)^2*(4*x  1)).  Colin Barker, Aug 15 2014
From Robert Israel, Feb 01 2019: (Start)
Conjecture and empirical g.f. verified.
a(n) = 4^(n+1)/3  (2*n+2)*2^n + (n^2+3*n)/2 + 2/3. (End)


MAPLE

seq(4^(n+1)/3  (2*n+2)*2^n + (n^2+3*n)/2 + 2/3, n=2..100); # Robert Israel, Feb 01 2019


MATHEMATICA

f[k_] := 2^k  1; t[n_] := Table[f[k], {k, 1, n}]
a[n_] := SymmetricPolynomial[2, t[n]]
Table[a[n], {n, 2, 32}] (* A203242 *)


CROSSREFS

Cf. A203241.
Sequence in context: A060416 A333368 A060425 * A121099 A197746 A342260
Adjacent sequences: A203239 A203240 A203241 * A203243 A203244 A203245


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Dec 31 2011


STATUS

approved



