A182956 G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n/(1+x)^(n*(3*n+1)/2).

1, 1, 3, 19, 206, 3324, 72951, 2050623, 70794951, 2911448386, 139376166446, 7628685374172, 470631647696157, 32346417958899335, 2452988261647043436, 203594274671070109776, 18366854200080039470784, 1790264247095540545539321

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..335

Formula

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.

Example

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 +...

Mathematica

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 *)

Prog

(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))}
(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)))}

Crossrefs

Cf. A133316, A182951, A182952, A141761.

Sequence in context: A230321 A108993 A245308 * A052886 A180563 A294330

Adjacent sequences: A182953 A182954 A182955 * A182957 A182958 A182959

Keyword

nonn

Author

Paul D. Hanna, Dec 31 2010

Status

approved