OFFSET
0,5
COMMENTS
Number of even entries in n-th row of triangle of Stirling numbers of the second kind (A048993).
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: x * (2 - x)/(1 - x)^2 - x * (1 + x) * Product_{k>=0} (1 + x^(2^k) + x^(2^(k+1))).
a(n) = n + 1 - A007306(n).
MATHEMATICA
Table[n + 1 - Sum[Mod[StirlingS2[n, k], 2], {k, 0, n}], {n, 0, 76}]
nmax = 76; CoefficientList[Series[x (2 - x)/(1 - x)^2 - x (1 + x) Product[(1 + x^(2^k) + x^(2^(k + 1))), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
PROG
(PARI) a(n) = n + 1 - sum(k=0, n, stirling(n, k, 2) % 2); \\ Michel Marcus, Jul 19 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 19 2019
STATUS
approved