A339057 - OEIS

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A339057

a(n) = (-1)^(n + 1)*3^(2*n + 1)*Euler(2*n + 1, 1/3)*2^(valuation_{2}(2*(n + 1))), the Steinhaus-Euler sequence S_{3}(n).

1, 13, 121, 18581, 305071, 61203943, 4353296221, 6669149100757, 206772189255571, 128970681211645873, 24697503335329725121, 45583359018138184284551, 6235055851689626935206871, 7982707567621372702411448803, 2955418704408380517540605162821, 40101878131071637461151318174173269 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	LINKS	`Table of n, a(n) for n=0..15.` `Sandor Csörgö, Gordon Simons, On Steinhaus' resolution of the St. Petersburg paradox, Probab. Math. Statist. 14 (1993), 157-172. MR1321758 (96b:60017).`
	EXAMPLE	`The array of the general case S_{k}(n) starts:` `[k]` `[1] -1, -1, -1, -17, -31, -691, -5461, ... [-A002425]` `[2] 0, 0, 0, 0, 0, 0, 0, ...` `[3] 1, 13, 121, 18581, 305071, 61203943, 4353296221, ... [this seq.]` `[4] 2, 44, 722, 196888, 5746082, 2049374444, 259141449842, ...` `[5] 3, 99, 2523, 1074243, 48982293, 27296351769, 5393115879063, ...` `...`
	MAPLE	`GenEuler := k -> (n -> (-1)^n(-k)^(2n+1)euler(2n+1, 1/k)):` `Steinhaus := n -> 2^padic[ordp](2(n+1), 2):` `seq(Steinhaus(n)GenEuler(3)(n), n = 0..15);`
	MATHEMATICA	`GenEuler[n_, k_] := (-1)^n (-k)^(2 n + 1) EulerE[2 n + 1, 1/k] ;` `Steinhaus[n_] := 2^IntegerExponent[2*(n+1), 2];` `a[n_] := GenEuler[n, 3] Steinhaus[n]; Table[a[n], {n, 0, 15}]`
	CROSSREFS	`Cf. A002425, A339058.` `Sequence in context: A033470 A297594 A326569 * A016230 A327961 A278276` `Adjacent sequences: A339054 A339055 A339056 * A339058 A339059 A339060`
	KEYWORD	`nonn`
	AUTHOR	`Peter Luschny, Nov 27 2020`
	STATUS	`approved`

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Last modified January 23 01:37 EST 2021. Contains 340384 sequences. (Running on oeis4.)