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URL: https://oeis.org/A215149

⇱ A215149 - OEIS

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A215149
a(n) = n * (1 + 2^(n-1)).
5
0, 2, 6, 15, 36, 85, 198, 455, 1032, 2313, 5130, 11275, 24588, 53261, 114702, 245775, 524304, 1114129, 2359314, 4980755, 10485780, 22020117, 46137366, 96469015, 201326616, 419430425, 872415258, 1811939355, 3758096412, 7784628253, 16106127390, 33285996575, 68719476768, 141733920801, 292057776162
OFFSET
0,2
COMMENTS
Related to Bernoulli numbers.
Essentially the same as A135854.
FORMULA
a(n) = (A157809(n) - A164555(n)) / A027642(n).
a(n) = n (the nonnegative integers A001477(n)) + n*2^(n-1) (their binomial transform A001787(n)).
a(n+1) - a(n) = 2,4,9,21,... = A001792(n) + 1.
a(n+1) - 2*a(n) = 2 before A132045(n+1).
a(n) is the binomial transform of b(n) = 0,2,2,3,4,5,... = A001477(n) with 2 instead of 1. b(n) = (A164558(n) - A027641(n))/A027642(n)?
G.f.: x*(2-6*x+5*x^2) / ( (1-x)^2*(1-2*x)^2 ). - R. J. Mathar, Aug 06 2012
E.g.f.: x*exp(x)*(1 + exp(x)). - G. C. Greubel, Jan 18 2025
a(n) = n * A094373(n). - Alois P. Heinz, Jan 18 2025
MATHEMATICA
Table[n(1+2^(n-1)), {n, 0, 40}] (* or *) LinearRecurrence[{6, -13, 12, -4}, {0, 2, 6, 15}, 40] (* Harvey P. Dale, Oct 18 2013 *)
PROG
(PARI) a(n) = n*(1+2^(n-1)) \\ Michel Marcus, Mar 10 2013
(Magma) [n*(1 + 2^(n-1)): n in [0..40]]; // G. C. Greubel, Apr 19 2018
(Python)
def A215149(n): return n*(pow(2, n)+2)//2
print([A215149(n) for n in range(41)]) # G. C. Greubel, Jan 18 2025
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Aug 04 2012
STATUS
approved