A269661 a(n) = Product_{i=1..n} (5^i - 4^i).

1, 9, 549, 202581, 425622681, 4907003889249, 302963327126122509, 98490045052104040328301, 166544794872251942218390753281, 1451779137596368920662880897497387769, 64798450159010700654830227323217753649135349

Offset

1,2

Links

Table of n, a(n) for n=1..11.

Formula

a(n) = Product_{i=1..n} A005060(i).

a(n) = 5^(binomial(n+1,2))*(4/5;4/5)_{n}, where (a;q)_{n} is the q-Pochhammer symbol. - G. C. Greubel, Mar 05 2016

a(n) ~ c * 5^(n*(n+1)/2), where c = QPochhammer(4/5) = 0.00336800585242312126... . - Vaclav Kotesovec, Oct 10 2016

Mathematica

Table[Product[5^i - 4^i, {i, n}], {n, 15}] (* Vincenzo Librandi, Mar 03 2016 *)
Table[5^(Binomial[n + 1, 2]) *QPochhammer[4/5, 4/5, n], {n, 1, 20}] (* G. C. Greubel, Mar 05 2016 *)
FoldList[Times, Table[5^n-4^n, {n, 15}]] (* Harvey P. Dale, Aug 28 2018 *)

Prog

(Magma) [&*[ 5^k-4^k: k in [1..n] ]: n in [1..16]]; // Vincenzo Librandi, Mar 03 2016
(PARI) a(n) = prod(k=1, n, 5^k-4^k); \\ Michel Marcus, Mar 05 2016

Crossrefs

Cf. A005060, A109345.

Cf. sequences of the form Product_{i=1..n}(j^i - 1): A005329 (j=2), A027871 (j=3), A027637 (j=4), A027872 (j=5), A027873 (j=6), A027875 (j=7), A027876 (j=8), A027877 (j=9), A027878 (j=10), A027879 (j=11), A027880 (j=12).

Cf. sequences of the form Product_{i=1..n}(j^i - k^1), k>1: A263394 (j=3, k=2), A269576 (j=4, k=3).

Sequence in context: A281800 A266889 A054608 * A287043 A317347 A357229

Adjacent sequences: A269658 A269659 A269660 * A269662 A269663 A269664

Keyword

nonn,easy

Author

Bob Selcoe, Mar 02 2016

Status

approved