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 A167660 Chocolate dove bar numerator: a(n) = (Sum_{k=0..floor(n/2)} k*binomial(n+k,k)*binomial(n,n-2*k)) + (Sum_{k=0..ceiling(n/2)} k*binomial(n+k-1,k-1)*binomial(n,n-2*k+1)). 1
 0, 1, 5, 23, 104, 458, 1987, 8523, 36248, 153134, 643466, 2691926, 11220156, 46620412, 193190831, 798700531, 3295291440, 13571239766, 55801698214, 229113328722, 939486081152, 3847872039340, 15742988692542, 64347264994238 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..500 D. M. Einstein, C. C. Heckman and T. S. Norfolk, On Sara's Dove Bar Habit D. M. Einstein, C. C. Heckman, and T. S. Norfolk, On Sara's Dove Bar Habit, American Mathematical Monthly, Nov. 2009, p. 831. FORMULA Recurrence: 2*(n-2)*n*a(n) = (3*n^2 + 9*n - 28)*a(n-1) + 2*(9*n^2 - 33*n + 22)*a(n-2) + 4*(n-1)*(2*n-5)*a(n-3). - Vaclav Kotesovec, Oct 20 2012 a(n) ~ 4^n*sqrt(n)/(3*sqrt(Pi)). - Vaclav Kotesovec, Oct 20 2012 MATHEMATICA a[n_]:= Sum[k*Binomial[n + k, k]*Binomial[n, n - 2*k], {k, 0, Floor[ n/2]}] + Sum[k*Binomial[n + k - 1, k - 1]* Binomial[n, n - 2*k + 1], {k, 0, Floor[(n + 1)/2]}]; Table[a[n], {n, 0, 30}] PROG (PARI) sum(k=0, n\2, k*binomial(n+k, k)*binomial(n, n-2*k)) + sum(k=0, (n+1)\2, k*binomial(n+k-1, k-1)*binomial(n, n-2*k+1)) CROSSREFS The denominator is A000984. Sequence in context: A102285 A218985 A129162 * A290924 A026760 A064914 Adjacent sequences:  A167657 A167658 A167659 * A167661 A167662 A167663 KEYWORD nonn,frac AUTHOR Roger L. Bagula, Nov 08 2009 EXTENSIONS Edited by Charles R Greathouse IV, Nov 09 2009 STATUS approved

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Last modified September 21 05:02 EDT 2021. Contains 347596 sequences. (Running on oeis4.)