A309014 a(n) = Sum_{k=0..n} (-1)^(n-k) * (Stirling2(n,k) mod 2).

1, 1, 0, 1, 1, 2, 1, 1, 2, 3, 1, 2, 3, 3, 2, 1, 3, 4, 1, 3, 4, 5, 3, 2, 5, 5, 2, 3, 5, 4, 3, 1, 4, 5, 1, 4, 5, 7, 4, 3, 7, 8, 3, 5, 8, 7, 5, 2, 7, 7, 2, 5, 7, 8, 5, 3, 8, 7, 3, 4, 7, 5, 4, 1, 5, 6, 1, 5, 6, 9, 5, 4, 9, 11, 4, 7, 11, 10, 7, 3, 10, 11, 3, 8, 11, 13, 8, 5, 13, 12, 5

Offset: 0

Author

Ilya Gutkovskiy, Jul 06 2019

Keywords

• nonn

Crossrefs

Cf. A001316, A002487, A007306, A008277, A048993, A060632, A070990.

Programs

Mathematica

Table[Sum[(-1)^(n - k) Mod[StirlingS2[n, k], 2], {k, 0, n}], {n, 0, 90}]
nmax = 90; CoefficientList[Series[1 + x (1 + x^3) Product[(1 + x^(2^k) + x^(2^(k + 1))), {k, 1, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

PARI

a(n) = sum(k=0, n, (-1)^(n-k) * (stirling(n,k,2) % 2)); \\ Michel Marcus, Jul 06 2019

Formula

G.f.: 1 + x * (1 + x^3) * Product_{k>=1} (1 + x^(2^k) + x^(2^(k+1))).

a(0) = 1; a(2*k+1) = A002487(k+1); a(2*k+2) = A002487(k).