%I A101853
%S A101853 6,18,37,64,100,146,203,272,354,450,561,688,832,994,1175,1376,1598,1842,
%T A101853 2109,2400,2716,3058,3427,3824,4250,4706,5193,5712,6264,6850,7471,8128,
%U A101853 8822,9554,10325,11136,11988,12882,13819,14800
%N A101853 4th partial summation within series as series accumulate n times from 
               an initial sequence of Euler Triangle's row 3: 1,4,1.
%H A101853 C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, 
               Explorations and Formulas of the Euler/Pascal Cube</a>.
%F A101853 a(1)=1; a(n) = (10*z)/3 + (5*z^2)/2 + z^3/6
%e A101853 n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ...
%e A101853 1 1 1 1 1 1 1 1 1 1 1
%e A101853 4 5 6 7 8 9 10 11 12 13 14
%e A101853 1 6 12 19 27 36 46 57 69 82 96
%e A101853 0 6 18 37 64 100 146 203 272 354 450 <- 4th
%e A101853 0 6 24 61 125 225 371 574 846 1200 1650
%e A101853 0 6 30 91 216 441 812 1386 2232 3432 5082
%e A101853 0 6 36 127 343 784 1596 2982 5214 8646 13728
%e A101853 0 6 42 169 512 1296 2892 5874 11088 19734 33462
%e A101853 0 6 48 217 729 2025 4917 10791 21879 41613 75075
%e A101853 ... ... ... ... ... ... ... ... ... ...
%e A101853 of each of the series
%Y A101853 Sequence in context: A028896 A034857 A116367 this_sequence A132432 A005899 
               A129863
%Y A101853 Adjacent sequences: A101850 A101851 A101852 this_sequence A101854 A101855 
               A101856
%K A101853 easy,nonn,uned
%O A101853 1,1
%A A101853 Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004