A208829 G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n / Product_{k=1..n} (1 + k*x)^2.

1, 1, 3, 16, 128, 1396, 19524, 335676, 6880388, 164277924, 4487230004, 138213671308, 4744574123684, 179758555018740, 7455418866550084, 336136394342220156, 16376124700916059428, 857610538194682984548, 48057661232590025818356, 2869922852119148564815692

Offset

0,3

Comments

Compare g.f. to: 1/(1-x) = Sum_{n>=0} n!*x^n/Product_{k=1..n} (1 + k*x).

Links

Table of n, a(n) for n=0..19.

Example

G.f.: 1/(1-x) = 1 + 1*x/(1+x)^2 + 3*x^2/((1+x)*(1+2*x))^2 + 16*x^3/((1+x)*(1+2*x)*(1+3*x))^2 + 128*x^4/((1+x)*(1+2*x)*(1+3*x)*(1+4*x))^2 +...

Prog

(PARI) {a(n)=if(n==0, 1, 1-polcoeff(sum(k=0, n-1, a(k)*x^k/prod(j=1, k, 1+j*x+x*O(x^n))^2), n))}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A118804, A215529.

Sequence in context: A088358 A082161 A264636 * A289145 A340341 A362661

Adjacent sequences: A208826 A208827 A208828 * A208830 A208831 A208832

Keyword

nonn

Author

Paul D. Hanna, Mar 01 2012

Status

approved