The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A097910

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A097910

Number of parts in all compositions of n into distinct parts.
(history; published version)

#34 by Alois P. Heinz at Mon Aug 10 08:59:19 EDT 2020

STATUS

editing

approved

#33 by Alois P. Heinz at Mon Aug 10 08:59:13 EDT 2020

MAPLE

end:

a:= proc(n) local l; l:=[b(n, n)];

add(i*l[i+1]*i!, i=1..nops(l)-1)

a:= n-> (l-> add(i*l[i+1]*i!, i=1..nops(l)-1))([b(n$2)]):

STATUS

approved

editing

#32 by Alois P. Heinz at Mon Aug 10 08:40:01 EDT 2020

STATUS

editing

approved

#31 by Alois P. Heinz at Mon Aug 10 08:39:42 EDT 2020

CROSSREFS

Cf. A001792, A008289, A015723, A032020, A072574, A336875.

STATUS

approved

editing

#30 by Alois P. Heinz at Mon Aug 10 08:35:10 EDT 2020

STATUS

editing

approved

#29 by Alois P. Heinz at Mon Aug 10 08:34:48 EDT 2020

FORMULA

a(n) = Sum_{k>=1..floor((sqrt(8*n+1)-1)/2)} k! * k * A008289(n,k). - Alois P. Heinz, Aug 10 2020

#28 by Alois P. Heinz at Mon Aug 10 08:33:40 EDT 2020

FORMULA

a(n) = Sum_{k>=1} k! * k * A008289(n,k). - Alois P. Heinz, Aug 10 2020

CROSSREFS

Cf. A001792, A008289, A015723, A032020, A336875.

STATUS

approved

editing

#27 by OEIS Server at Mon Aug 10 08:28:07 EDT 2020

LINKS

Alois P. Heinz, <a href="/A097910/b097910_1.txt">Table of n, a(n) for n = 1..5000</a>

#26 by Alois P. Heinz at Mon Aug 10 08:28:07 EDT 2020

STATUS

editing

approved

Discussion

Mon Aug 10

08:28

OEIS Server: Installed new b-file as b097910.txt.  Old b-file is now b097910_1.txt.

#25 by Alois P. Heinz at Mon Aug 10 08:27:44 EDT 2020

LINKS

Alois P. Heinz, <a href="/A097910/b097910_1.txt">Table of n, a(n) for n = 1..10005000</a>

MAPLE

b:= proc(n, i, kp) option remember; `if`(i*(i+1)/2<k or n>, 0,

(2*i-k+1)*k/2, 0, `if`(n=0, [p!*p, b(n-i, min(n-i, i-1), p+1, 0], )+b(n, i-1, kp)))+

(p-> p+[0, p[1]])(b(n-i, min(n-i, i-1), k-1))))

a:= n-> add(b(n$2, k)[2]*k!, k=1..floor((sqrt(8*n+1)-1)/2)):

a:= n-> b(n$2, 0):

seq(a(n), n=10..50); # Alois P. Heinz, Aug 06 10 2020

STATUS

approved

editing