%I
%S 1,1,2,3,6,10,20,35,56,84,210,330,495,715,1001,3003,4368,6188,8568,
%T 11628,15504,54264,74613,100947,134596,177100,230230,296010,1184040,
%U 1560780,2035800,2629575,3365856,4272048,5379616,6724520,30260340
%N a(n) = binomial(n, A002024(n+1)1) where A002024 is "n appears n times".
%H Paul D. Hanna, <a href="/A180272/b180272.txt">Table of n, a(n) for n = 0..1000</a>
%e G.f.: A(x) = 1 + x + 2*x^2 + 3*x^3 + 6*x^4 + 10*x^5 + 20*x^6 +...
%e Terms are shown below in parenthesis as they appear in Pascals triangle:
%e (1);
%e 1,(1);
%e 1,(2),1;
%e 1,3,(3),1;
%e 1,4,(6),4,1;
%e 1,5,(10),5,1;
%e 1,6,15,(20),15,6,1;
%e 1,7,21,(35),35,21,7,1;
%e 1,8,28,(56),70,56,28,8,1;
%e 1,9,36,(84),126,126,84,36,9,1;
%e 1,10,45,120,(210),252,210,120,45,10,1; ...
%o (PARI) {a(n)=binomial(n,(sqrtint(8*n+1)1)\2)}
%Y Cf. A002024.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jan 17 2011
