OFFSET
0,3
FORMULA
a(n) = -Sum_{k=0..n}(C(n,k)*Euler(n+k+1)). - Vladimir Kruchinin, Apr 06 2015
a(n) ~ (-1)^(n+1) * 2^(4*n+9/2) * n^(2*n+3/2) / (exp(2*n) * Pi^(2*n+3/2)). - Vaclav Kotesovec, Apr 06 2015
EXAMPLE
a(n) is the main diagonal in this difference table D(n, k):
[ 0, 0, 1, -3, -5, 45, 61, -1113, -1385]
[ 0, 1, -2, -8, 40, 106, -1052, -2498]
[ 1, -1, -10, 32, 146, -946, -3550]
[ 0, -11, 22, 178, -800, -4496]
[ -11, 11, 200, -622, -5296]
[ 0, 211, -422, -5918]
[ 211, -211, -6340]
[ 0, -6551]
[-6551]
D(n, 0) = A240560(n).
D(0, n) = A240559(n).
D(2*n, 0) = (-1)^(n+1)*A147315(2*n, 2).
MAPLE
MATHEMATICA
Table[-Sum[Binomial[n, k]*EulerE[n+k+1], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Apr 06 2015 *)
PROG
(Maxima)
a(n):=-sum(binomial(n, k)*euler(n+k+1), k, 0, n); /* Vladimir Kruchinin, Apr 06 2015 */
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Apr 17 2014
STATUS
approved