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A209275
a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8 + 9*n^9.
1
1, 45, 8193, 250957, 3029217, 21362301, 106420465, 415866333, 1358612097, 3868151437, 9876543201, 23084307885, 50147947873, 102436518237, 198541656657, 367761728701, 654820258305, 1126121592813, 1877892797377, 3046610084877
OFFSET
0,2
COMMENTS
The smallest prime here is a(12) = 50147947873.
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: (3*x^9 +3153*x^8 +104852*x^7 +706780*x^6 +1389234*x^5 +883142*x^4 +170932*x^3 +7788*x^2 +35*x +1) / (x -1)^10. - Colin Barker, Apr 19 2013
EXAMPLE
a(2) = 1 + 2*2^2 + 3*2^3 + 4*2^4 + 5*2^5 + 6*2^6 + 7*2^7 + 8*2^8 + 9*2^9 = 8193.
MATHEMATICA
Table[Total[Table[i*n^i, {i, 2, 9}]]+1, {n, 0, 30}] (* Harvey P. Dale, Jan 26 2013 *)
PROG
(PARI) for(n=0, 30, print1(1 + sum(k=2, 9, k*n^k), ", ")) \\ G. C. Greubel, Jan 04 2018
(Magma) [1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8 + 9*n^9: n in [0..30]]; // G. C. Greubel, Jan 04 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Jan 15 2013
STATUS
approved