A309256 a(n) = n + 1 - Sum_{k=0..n} (Stirling2(n,k) mod 2).

0, 1, 1, 1, 2, 2, 2, 3, 5, 5, 4, 4, 6, 7, 7, 9, 12, 12, 10, 9, 11, 11, 10, 12, 16, 17, 15, 15, 18, 20, 20, 23, 27, 27, 24, 22, 24, 23, 21, 23, 28, 28, 24, 23, 27, 29, 28, 32, 38, 39, 35, 33, 36, 36, 34, 37, 43, 45, 42, 42, 46, 49, 49, 53, 58, 58, 54, 51, 53, 51, 48, 50, 56, 55, 49, 47, 52

Offset: 0

Author

Ilya Gutkovskiy, Jul 19 2019

Keywords

• nonn

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

Crossrefs

Cf. A002487, A007306, A048967, A048993, A309255.

Programs

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]

PARI

a(n) = n + 1 - sum(k=0, n, stirling(n, k, 2) % 2); \\ Michel Marcus, Jul 19 2019

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).