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A336896 Sum of the leftmost parts in all compositions of n into distinct parts. 1
0, 1, 2, 6, 8, 15, 30, 42, 64, 99, 190, 242, 384, 533, 798, 1380, 1824, 2635, 3762, 5320, 7280, 12327, 15554, 22632, 30720, 43425, 57538, 80730, 122920, 159239, 220830, 299150, 406656, 542883, 733278, 962710, 1443600, 1820437, 2496638, 3280992, 4451120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also sum of the rightmost parts in all compositions of n into distinct parts.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

FORMULA

a(n) = n * Sum_{k=1..floor((sqrt(8*n+1)-1)/2)} (k-1)! * A008289(n,k).

a(n) = n * A032153(n).

EXAMPLE

a(6) = 30 = 1 + 1 + 2 + 2 + 3 + 3 + 2 + 4 + 1 + 5 + 6: (1)23, (1)32, (2)13, (2)31, (3)12, (3)21, (2)4, (4)2, (1)5, (5)1, (6).

MAPLE

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

     `if`(n=0, p!, b(n, i-1, p)+b(n-i, min(n-i, i-1), p+1)))

    end:

a:= n-> `if`(n=0, 0, n*b(n$2, -1)):

seq(a(n), n=0..50);

CROSSREFS

Cf. A000225 (the same for all compositions), A008289, A032020, A032153.

Sequence in context: A049818 A066189 A278834 * A306906 A174658 A326300

Adjacent sequences:  A336893 A336894 A336895 * A336897 A336898 A336899

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 07 2020

STATUS

approved

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Last modified June 18 11:58 EDT 2021. Contains 345098 sequences. (Running on oeis4.)