login
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
OFFSET
0,3
LINKS
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
KEYWORD
nonn,frac
AUTHOR
Roger L. Bagula, Nov 08 2009
EXTENSIONS
Edited by Charles R Greathouse IV, Nov 09 2009
STATUS
approved