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%I #10 Aug 11 2014 22:45:29
%S 0,0,0,0,0,0,0,0,0,1,11,67,304,1164,4014,12883,39020,112031,305373,
%T 791546,1956250,4626271,10512977,23062285,49074852,101805531,
%U 206954478,414408128,821558374,1620083727,3190286294,6291416560,12444470904,24698286376,49154868690
%N Unique sequence that begins with nine zeros and a 1 and has the properties that each leading term of the difference triangle is single-digit, and the concatenation of the leading terms of the difference triangle is the same as the concatenation of the digits of the sequence.
%C Binomial transform of sequence gives successive digits of sequence.
%H Nathaniel Johnston, <a href="/A125591/b125591.txt">Table of n, a(n) for n = 0..189</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%e Difference triangle begins:
%e 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 11, 67, 304, 1164, 4014, 12883, 39020
%e 0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 56, 237, 860, 2850, 8869, 26137
%e 0, 0, 0, 0, 0, 0, 0, 1, 9, 46, 181, 623, 1990, 6019, 17268
%e 0, 0, 0, 0, 0, 0, 1, 8, 37, 135, 442, 1367, 4029, 11249
%e 0, 0, 0, 0, 0, 1, 7, 29, 98, 307, 925, 2662, 7220
%e 0, 0, 0, 0, 1, 6, 22, 69, 209, 618, 1737, 4558
%e 0, 0, 0, 1, 5, 16, 47, 140, 409, 1119, 2821
%e 0, 0, 1, 4, 11, 31, 93, 269, 710, 1702
%e 0, 1, 3, 7, 20, 62, 176, 441, 992
%e 1, 2, 4, 13, 42, 114, 265, 551
%e 1, 2, 9, 29, 72, 151, 286
%e 1, 7, 20, 43, 79, 135
%Y Cf. A125588.
%K nonn,base,easy
%O 0,11
%A _N. J. A. Sloane_, Jan 07 2007
%E Name edited and a(17) - a(34) from _Nathaniel Johnston_, Apr 15 2011
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