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A309014 a(n) = Sum_{k=0..n} (-1)^(n-k) * (Stirling2(n,k) mod 2). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 20:55 EDT 2020. Contains 337182 sequences. (Running on oeis4.)