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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 `if`(n=0, 1, b(n^2+1, 1, 0, n+1)): seq(a(n), n=0..10); 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^2 + 1, 1, 0, n + 1]]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, May 21 2018, translated from Maple *) CROSSREFS Main diagonal of A294746. Cf. A002522. Sequence in context: A024139 A316397 A291332 * A199354 A276241 A233250 Adjacent sequences:  A294744 A294745 A294746 * A294748 A294749 A294750 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 07 2017 STATUS approved

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Last modified August 18 06:30 EDT 2018. Contains 313823 sequences. (Running on oeis4.)