The On-Line Encyclopedia of Integer Sequences (OEIS)

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A327290

Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size seven are used and the colors are introduced in increasing order.
(history; published version)

#7 by Vaclav Kotesovec at Wed Sep 18 12:38:56 EDT 2019

STATUS

editing

approved

#6 by Vaclav Kotesovec at Wed Sep 18 12:38:53 EDT 2019

FORMULA

a(n) ~ exp(sqrt(2*(Pi^2 - 6*polylog(2,-6))*n/3)) * sqrt(Pi^2 - 6*polylog(2,-6)) / (4*7!*sqrt(21)*Pi*n). - Vaclav Kotesovec, Sep 18 2019

STATUS

approved

editing

#5 by Alois P. Heinz at Thu Aug 29 11:40:34 EDT 2019

STATUS

editing

approved

#4 by Alois P. Heinz at Thu Aug 29 11:40:31 EDT 2019

LINKS

Alois P. Heinz, <a href="/A327290/b327290.txt">Table of n, a(n) for n = 28..5000</a>

#3 by Alois P. Heinz at Wed Aug 28 16:32:32 EDT 2019

NAME

7

Number of partitions of n into colored blocks of equal parts, such that all colors from a set of size seven are used and the colors are introduced in increasing order.

MAPLE

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

(t-> b(t, min(t, i-1), k))(n-i*j), j=1..n/i)*k+b(n, i-1, k)))

end:

a:= n-> (k-> add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k)/k!)(7):

seq(a(n), n=28..65);

#2 by Alois P. Heinz at Wed Aug 28 14:25:46 EDT 2019

NAME

allocated for Alois P. Heinz

7

DATA

1, 2, 5, 10, 20, 36, 65, 110, 204, 337, 573, 934, 1527, 2416, 3826, 5907, 9088, 13963, 21070, 31642, 47131, 69707, 102214, 149143, 215754, 310547, 443840, 633139, 895294, 1262971, 1770236, 2473601, 3436809, 4761393, 6561269, 9015761, 12330231, 16812326

OFFSET

28,2

CROSSREFS

Column k=7 of A321878.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Aug 28 2019

STATUS

approved

editing

#1 by Alois P. Heinz at Wed Aug 28 14:17:32 EDT 2019

NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved