The On-Line Encyclopedia of Integer Sequences (OEIS)

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A294985

Number of compositions (ordered partitions) of 1 into exactly 6n+1 powers of 1/(n+1).
(history; published version)

#10 by Vaclav Kotesovec at Fri Sep 20 05:06:15 EDT 2019

STATUS

editing

approved

#9 by Vaclav Kotesovec at Fri Sep 20 05:06:10 EDT 2019

FORMULA

a(n) ~ 6^(6*n + 3/2) / (2*Pi*n)^(5/2). - Vaclav Kotesovec, Sep 20 2019

STATUS

approved

editing

#8 by Bruno Berselli at Mon May 21 04:14:21 EDT 2018

STATUS

reviewed

approved

#7 by Joerg Arndt at Mon May 21 03:58:09 EDT 2018

STATUS

proposed

reviewed

#6 by Jean-François Alcover at Mon May 21 03:35:02 EDT 2018

STATUS

editing

proposed

#5 by Jean-François Alcover at Mon May 21 03:34:59 EDT 2018

MATHEMATICA

b[n_, r_, p_, k_] := b[n, r, p, k] = If[n < r, 0, If[r == 0, If[n == 0, p!, 0], Sum[b[n - j, k*(r - j), p + j, k]/j!, {j, 0, Min[n, r]}]]];

a[n_] := If[n == 0, 1, b[#*n + 1, 1, 0, n + 1]]&[6];

Table[a[n], {n, 0, 15}] (* Jean-François Alcover, May 21 2018, translated from Maple *)

STATUS

approved

editing

#4 by Alois P. Heinz at Sun Nov 12 10:01:09 EST 2017

STATUS

editing

approved

#3 by Alois P. Heinz at Sun Nov 12 10:01:05 EST 2017

LINKS

Alois P. Heinz, <a href="/A294985/b294985.txt">Table of n, a(n) for n = 0..215</a>

#2 by Alois P. Heinz at Sun Nov 12 09:59:25 EST 2017

NAME

allocated for Alois P. Heinz

Number of compositions (ordered partitions) of 1 into exactly 6n+1 powers of 1/(n+1).

DATA

1, 4347, 40647178, 701954099115, 16596702491586251, 461871979542736134676, 14138484434475011392912026, 460977928965130046448503507051, 15732393344641740454307566725567376, 556054452693724489326948624520266970011, 20208669423838553069878798723999482271266772

OFFSET

0,2

MAPLE

b:= proc(n, r, p, k) option remember;

`if`(n<r, 0, `if`(r=0, `if`(n=0, p!, 0), add(

b(n-j, k*(r-j), p+j, k)/j!, j=0..min(n, r))))

end:

a:= n-> (k-> `if`(n=0, 1, b(k*n+1, 1, 0, n+1)))(6):

seq(a(n), n=0..15);

CROSSREFS

Row n=6 of A294746.

KEYWORD

allocated

nonn

AUTHOR

Alois P. Heinz, Nov 12 2017

STATUS

approved

editing

#1 by Alois P. Heinz at Sun Nov 12 09:42:46 EST 2017

NAME

allocated for Alois P. Heinz

KEYWORD

allocated

STATUS

approved