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A294982 Number of compositions (ordered partitions) of 1 into exactly 3n+1 powers of 1/(n+1). 2
1, 13, 217, 4245, 90376, 2019836, 46570140, 1097525253, 26293568950, 638048716305, 15643738390215, 386826618273420, 9633468179090952, 241366000080757480, 6078975012187601768, 153798067122829610085, 3906583987216447704594, 99579591801208823965115 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..700

EXAMPLE

a(0) = 1: [1].

a(1) = 13: [1/4,1/4,1/4,1/4], [1/2,1/4,1/8,1/8], [1/2,1/8,1/4,1/8], [1/2,1/8,1/8,1/4], [1/4,1/2,1/8,1/8], [1/4,1/8,1/2,1/8], [1/4,1/8,1/8,1/2], [1/8,1/2,1/4,1/8], [1/8,1/2,1/8,1/4], [1/8,1/4,1/2,1/8], [1/8,1/4,1/8,1/2], [1/8,1/8,1/2,1/4], [1/8,1/8,1/4,1/2].

MAPLE

a:= proc(n) option remember; `if`(n<2, 12*n+1, (3*n-1)*(3*n+1)*

      3*((15*n^3-31*n^2-4*n+8)*n*a(n-1)-3*(3*n-4)*(3*n-2)*

      (3*n^2-2*n-2)*a(n-2))/((n+1)*(4*n+2)*(3*n^2-8*n+3)*n^2))

    end:

seq(a(n), n=0..20);

MATHEMATICA

a[n_] := a[n] = If[n < 2, 12*n + 1, (3*n - 1)*(3*n + 1)*3*((15*n^3 - 31*n^2 - 4*n + 8)*n*a[n-1] - 3*(3*n - 4)*(3*n - 2)*(3*n^2 - 2*n - 2)*a[n-2])/((n + 1)*(4*n + 2)*(3*n^2 - 8*n + 3)*n^2)];

Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, May 21 2018, translated from Maple *)

CROSSREFS

Row n=3 of A294746.

Sequence in context: A140517 A096141 A218475 * A320627 A059525 A086147

Adjacent sequences:  A294979 A294980 A294981 * A294983 A294984 A294985

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 12 2017

STATUS

approved

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Last modified August 17 11:14 EDT 2019. Contains 326057 sequences. (Running on oeis4.)