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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 Seiichi Manyama, Table of n, a(n) for n = 0..467 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. Cf. A036968, A083007, A083008, A083010, A083011, A083012, A083013, A083014. Sequence in context: A264471 A264477 A223357 * A365111 A190968 A127416 Adjacent sequences: A083006 A083007 A083008 * A083010 A083011 A083012 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.)