A187740 G.f.: Sum_{n>=0} (5*n+1)^n * x^n / (1 + (5*n+1)*x)^n.

1, 6, 85, 1650, 40500, 1200000, 41625000, 1653750000, 74025000000, 3685500000000, 201993750000000, 12084187500000000, 783523125000000000, 54729675000000000000, 4097124281250000000000, 327237848437500000000000, 27775310062500000000000000, 2496585341250000000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = (5*n+7) * 5^(n-1) * n!/2 for n>0 with a(0)=1.

E.g.f.: (2 - 8*x + 15*x^2) / (2*(1-5*x)^2).

Example

 G.f.: A(x) = 1 + 6*x + 85*x^2 + 1650*x^3 + 40500*x^4 + 1200000*x^5 +...
where
A(x) = 1 + 6*x/(1+6*x) + 11^2*x^2/(1+11*x)^2 + 16^3*x^3/(1+16*x)^3 + 21^4*x^4/(1+21*x)^4 + 26^5*x^5/(1+26*x)^5 +...

Prog

 (PARI) {a(n)=polcoeff(sum(m=0, n, ((5*m+1)*x)^m/(1+(5*m+1)*x +x*O(x^n))^m), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A187735, A014479, A187738, A187739, A221160, A221161.

Sequence in context: A164266 A136597 A064329 * A332407 A358297 A209035

Adjacent sequences: A187737 A187738 A187739 * A187741 A187742 A187743

Keyword

nonn

Author

Paul D. Hanna, Jan 03 2013

Status

approved