A276489 a(n) = 25^(n+1)*Gamma(n+8/5)/Gamma(3/5).

15, 600, 39000, 3510000, 403650000, 56511000000, 9324315000000, 1771619850000000, 380898267750000000, 91415584260000000000, 24225129828900000000000, 7025287650381000000000000, 2212965609870015000000000000, 752408307355805100000000000000, 274629032184868861500000000000000

Offset

0,1

Links

Table of n, a(n) for n=0..14.

Formula

E.g.f.: 15/(1 - 25*x)^(8/5).

D-finite with recurrence: a(n) = 5*(5*n + 3)*a(n - 1), a(0)=15.

a(n) = Product_{k=0..n} 5*(5*k + 3).

a(n) = Product_{k=0..n} 5*A016885(k).

a(n) ~ sqrt(2*Pi)*25^(n+1)*n^(n+11/10)/(Gamma(3/5)*exp(n)).

Sum_{n>=0} 1/a(n) = exp(1/25)*(Gamma(3/5) - Gamma(3/5, 1/25))/5^(4/5)

= 0.06835926175445652444604..., where Gamma(a, x) is the incomplete Gamma function.

Example

a(0) = (1+2+3+4+5) = 15;
a(1) = (1+2+3+4+5)*(6+7+8+9+10) = 600;
a(2) = (1+2+3+4+5)*(6+7+8+9+10)*(11+12+13+14+15) = 39000, etc.

Mathematica

FullSimplify[Table[25^(n + 1) (Gamma[n + 8/5]/Gamma[3/5]), {n, 0, 14}]]

Prog

(PARI) a(n) = prod(k=0, n, 5*(5*k + 3)); \\ Michel Marcus, Sep 06 2016

Crossrefs

Cf. A016885, A268730.

Sequence in context: A343074 A232291 A294834 * A243227 A215899 A027505

Adjacent sequences: A276486 A276487 A276488 * A276490 A276491 A276492

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Sep 05 2016

Status

approved