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 A180272 a(n) = binomial(n, A002024(n+1)-1) where A002024 is "n appears n times". 1

%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

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Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)