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