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%I #12 Jun 02 2018 18:14:14
%S 1,3,10,29,70,146,273,470,759,1165,1716,2443,3380,4564,6035,7836,
%T 10013,12615,15694,19305,23506,28358,33925,40274,47475,55601,64728,
%U 74935,86304,98920,112871,128248,145145,163659,183890,205941,229918,255930
%N Partial sums of A100119. Sum of first n of the n-th centered n-gonal numbers.
%C This is to n-th centered n-gonal numbers (A100119) as A101357 is to n-th n-gonal numbers (A060354). a(2) = 3 and a(4) = 29 are primes. a(39) = 284089 = 13^2 * 41^2.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (n*(26-3*n-2*n^2+3*n^3))/24. G.f.: x*(x^3-5*x^2+2*x-1) / (x-1)^5. - _Colin Barker_, Apr 29 2013
%e a(41) = 1 + 2 + 7 + 19 + 41 + 76 + 127 + 197 + 289 + 406 + 551 + 727 + 937 + 1184 + 1471 + 1801 + 2177 + 2602 + 3079 + 3611 + 4201 + 4852 + 5567 + 6349 + 7201 + 8126 + 9127 + 10207 + 11369 + 12616 + 13951 + 15377 + 16897 + 18514 + 20231 + 22051 + 23977 + 26012 + 28159 + 30421 + 32801 + 35302 = 382613.
%t LinearRecurrence[{5,-10,10,-5,1},{1,3,10,29,70},40] (* _Harvey P. Dale_, Jun 02 2018 *)
%Y Cf. A060354, A100119, A101357.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Aug 04 2007
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