A182956 - OEIS

%I #7 Jul 22 2014 16:30:58

%S 1,1,3,19,206,3324,72951,2050623,70794951,2911448386,139376166446,

%T 7628685374172,470631647696157,32346417958899335,2452988261647043436,

%U 203594274671070109776,18366854200080039470784,1790264247095540545539321

%N G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n/(1+x)^(n*(3*n+1)/2).

%H Vaclav Kotesovec, <a href="/A182956/b182956.txt">Table of n, a(n) for n = 0..335</a>

%F a(n) = 1 - Sum_{k=0..n-1} a(k)*(-1)^(n-k)*C(k(3k+1)/2 + n-k-1, n-k) for n>0, with a(0)=1.

%e 1/(1-x) = 1 + x/(1+x)^2 + 3*x^2/(1+x)^7 + 19*x^3/(1+x)^15 + 206*x^4/(1+x)^26 + 3324*x^5/(1+x)^40 + 72951*x^6/(1+x)^57 +...

%t nmax=20; b=ConstantArray[0,nmax+1]; b[[1]]=1; Do[b[[n+1]]=1-Sum[b[[j+1]]*(-1)^(n-j)*Binomial[j*(3*j+1)/2+n-j-1,n-j],{j,0,n-1}];,{n,1,nmax}]; b  (* _Vaclav Kotesovec_, Jul 22 2014 *)

%o (PARI) {a(n)=if(n==0,1,polcoeff(-(1-x)*sum(m=0,n-1,a(m)*x^m/(1+x +x*O(x^n))^(m*(3*m+1)/2)),n))}

%o (PARI) {a(n)=if(n==0, 1, 1 - sum(j=0, n-1, a(j)*(-1)^(n-j)*binomial(j*(3*j+1)/2+n-j-1, n-j)))}

%Y Cf. A133316, A182951, A182952, A141761.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 31 2010