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A083009 a(n) = Sum_{k=0,n-1} 5^k*B(k)*binomial(n,k) where B(k) is the k-th Bernoulli number. 9
0, 1, -4, 6, 16, -74, -264, 1946, 9056, -88434, -512024, 6154786, 42716496, -607884394, -4920817384, 80834386026, 747784582336, -13923204233954, -144898927180344, 3015393801263666, 34867899296006576, -801997872697905114, -10201104981227536904, 256982712667627683706 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
E.g.f.: 5x/(1+exp(x)+exp(2x)+exp(3x)+exp(4x)). - Benoit Cloitre, Oct 26 2012 (following I. Gessel).
MATHEMATICA
Range[0, 15]! CoefficientList[ Series[ 5x/(1 + Exp[x] + Exp[ 2x] + Exp[ 3x] + Exp[ 4x]), {x, 0, 15}], x] (* Robert G. Wilson v, Oct 26 2012 *)
Table[Sum[5^k*BernoulliB[k] Binomial[n, k], {k, 0, n - 1}], {n, 0, 23}] (* Michael De Vlieger, Sep 28 2016 *)
PROG
(PARI) a(n)=sum(k=0, n-1, 5^k*binomial(n, k)*bernfrac(k))
CROSSREFS
Cf. A001469.
Sequence in context: A264471 A264477 A223357 * A365111 A190968 A127416
KEYWORD
sign
AUTHOR
Benoit Cloitre, May 31 2003
EXTENSIONS
Offset changed to 0 by Seiichi Manyama, Sep 28 2016
STATUS
approved

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Last modified February 21 07:26 EST 2024. Contains 370219 sequences. (Running on oeis4.)