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

0,6

Links

Table of n, a(n) for n=0..90.

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).

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]

Prog

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

Crossrefs

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

Sequence in context: A286334 A118492 A079246 * A070990 A097868 A025830

Adjacent sequences: A309011 A309012 A309013 * A309015 A309016 A309017

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 06 2019

Status

approved