A226805 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.

1, 7, 70, 877, 13316, 237799, 4885980, 113566121, 2946476764, 84417530491, 2647176188372, 90183424037293, 3316840864313484, 130985236211745959, 5528094465439087876, 248308899812296990033, 11827417687501017074876, 595470029978391175571923

Offset: 1

Author

José María Grau Ribas, Jun 18 2013

Keywords

• nonn

Examples

			P_3(x) = 18 - 27*x + 10*x^2; a(3) = P_3(3+1) = 70.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A140119, A140118, A126130, A000312.

Programs

Mathematica

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}]
a[n_] := InterpolatingPolynomial[Table[{i, i^i}, {i, n}], n+1]; Array[a, 20] (* Giovanni Resta, Jun 18 2013 *)

PARI

a(n)=subst(polinterpolate(vector(n,i,i^i)),'x,n+1) \\ Charles R Greathouse IV, Nov 19 2013