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A309256 a(n) = n + 1 - Sum_{k=0..n} (Stirling2(n,k) mod 2). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Number of even entries in n-th row of triangle of Stirling numbers of the second kind (A048993).

LINKS

Table of n, a(n) for n=0..76.

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

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Last modified September 25 23:58 EDT 2021. Contains 347664 sequences. (Running on oeis4.)