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

0,5

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

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

Sequence in context: A304718 A036355 A228390 * A095972 A091974 A029073

Adjacent sequences: A309253 A309254 A309255 * A309257 A309258 A309259

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 19 2019

Status

approved