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%I #12 Nov 19 2013 14:18:00
%S 1,7,70,877,13316,237799,4885980,113566121,2946476764,84417530491,
%T 2647176188372,90183424037293,3316840864313484,130985236211745959,
%U 5528094465439087876,248308899812296990033,11827417687501017074876,595470029978391175571923
%N P_n(n+1) where P_n(x) is the polynomial of degree n-1 which satisfies P_n(i) = i^i for i = 1,...,n.
%H Alois P. Heinz, <a href="/A226805/b226805.txt">Table of n, a(n) for n = 1..100</a>
%e P_3(x) = 18 - 27*x + 10*x^2; a(3) = P_3(3+1) = 70.
%t P[n_][x_] = Sum[a[i]*x^i, {i, 0, n - 1}];ecu[n_] := Table[P[n][i] == i^i, {i, 1, n}];PP[n_][x_] := P[n][x] /. Solve[ecu[n]][[1]];Table[PP[i][i + 1], {i, 1, 22}]
%t a[n_] := InterpolatingPolynomial[Table[{i, i^i}, {i, n}], n+1]; Array[a, 20] (* _Giovanni Resta_, Jun 18 2013 *)
%o (PARI) a(n)=subst(polinterpolate(vector(n,i,i^i)),'x,n+1) \\ _Charles R Greathouse IV_, Nov 19 2013
%Y Cf. A140119, A140118, A126130, A000312.
%K nonn
%O 1,2
%A _José María Grau Ribas_, Jun 18 2013