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A293366 Number of partitions of n where each part i is marked with a word of length i over a binary alphabet whose letters appear in alphabetical order and both letters occur at least once in the partition. 3
3, 12, 40, 104, 279, 654, 1577, 3560, 8109, 17734, 39205, 83996, 181043, 382856, 811084, 1694468, 3545864, 7340308, 15205768, 31259422, 64253260, 131314502, 268332975, 545854344, 1110087515, 2250051262, 4558868119, 9213241988, 18613362500, 37529700206 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 2..1000

FORMULA

a(n) ~ c * 2^n, where c = A256155 = 18.563146563610114727475354232269284... - Vaclav Kotesovec, Oct 11 2017

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

      b(n, i-1, k)+`if`(i>n, 0, b(n-i, i, k)*binomial(i+k-1, k-1))))

    end:

a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k))(2):

seq(a(n), n=2..35);

CROSSREFS

Column k=2 of A261719.

Sequence in context: A034956 A032093 A007993 * A080929 A052482 A061136

Adjacent sequences:  A293363 A293364 A293365 * A293367 A293368 A293369

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 07 2017

STATUS

approved

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Last modified July 18 07:10 EDT 2019. Contains 325134 sequences. (Running on oeis4.)