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A294747 Number of compositions (ordered partitions) of 1 into exactly n^2+1 powers of 1/(n+1). 2
1, 1, 10, 4245, 216456376, 2713420774885145, 14138484434475011392912026, 46050764886573707269872023694736134925, 131223281654667714701311635640432890136981994039662720, 435699237793484726791774188056400878106883117166142375354233228879800569 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..26

FORMULA

a(n) = [x^((n+1)^n)] (Sum_{j=0..n^2+1} x^((n+1)^j))^(n^2+1) for n>0, a(0) = 1.

a(n) = A294746(n,n).

EXAMPLE

a(0) = 1: [1].

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

a(2) = 10 = binomial(5,2): [1/3,1/3,1/9,1/9,1/9], [1/3,1/9,1/3,1/9,1/9], [1/3,1/9,1/9,1/3,1/9], [1/3,1/9,1/9,1/9,1/3], [1/9,1/3,1/3,1/9,1/9], [1/9,1/3,1/9,1/3,1/9], [1/9,1/3,1/9,1/9,1/3], [1/9,1/9,1/3,1/3,1/9], [1/9,1/9,1/3,1/9,1/3], [1/9,1/9,1/9,1/3,1/3].

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-> `if`(n=0, 1, b(n^2+1, 1, 0, n+1)):

seq(a(n), n=0..10);

CROSSREFS

Main diagonal of A294746.

Cf. A002522.

Sequence in context: A249851 A024139 A291332 * A199354 A276241 A233250

Adjacent sequences:  A294744 A294745 A294746 * A294749 A294750 A294751

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 07 2017

STATUS

approved

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Last modified February 20 21:53 EST 2018. Contains 299387 sequences. (Running on oeis4.)