A009964 -id:A009964 - cp's OEIS frontend

A013812 a(n) = 20^(4*n + 1).

20, 3200000, 512000000000, 81920000000000000, 13107200000000000000000, 2097152000000000000000000000, 335544320000000000000000000000000, 53687091200000000000000000000000000000, 8589934592000000000000000000000000000000000, 1374389534720000000000000000000000000000000000000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (160000).

Subsequence of A009964.

Cf. A013776, A013792, A016813.

[20^(4*n+1): n in [0..15]]; // Vincenzo Librandi, Jul 06 2011

A013812:=n->20^(4*n+1): seq(A013812(n), n=0..10); # Wesley Ivan Hurt, Mar 31 2017

20^(4*Range[0,10]+1) (* or *) NestList[160000#&,20,10] (* Harvey P. Dale, Dec 30 2012 *)

a(n) = 160000*a(n-1). - Harvey P. Dale, Dec 30 2012
From Elmo R. Oliveira, Jul 13 2025: (Start)
G.f.: 20/(1-160000*x).
E.g.f.: 20*exp(160000*x).
a(n) = A013776(n)*A013792(n) = A009964(A016813(n)). (End)

A013813 a(n) = 20^(4*n + 3).

Original entry on oeis.org

8000, 1280000000, 204800000000000, 32768000000000000000, 5242880000000000000000000, 838860800000000000000000000000, 134217728000000000000000000000000000, 21474836480000000000000000000000000000000, 3435973836800000000000000000000000000000000000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (160000).

Subsequence of A009964.

Cf. A004767, A013777, A013793.

[20^(4*n+3): n in [0..15]]; // Vincenzo Librandi, Jul 06 2011

20^(4*Range[0, 10] + 3) (* or *)
NestList[160000*# &, 8000, 10] (* Paolo Xausa, Jul 21 2025 *)

From Elmo R. Oliveira, Jul 13 2025: (Start)
G.f.: 8000/(1-160000*x).
E.g.f.: 8000*exp(160000*x).
a(n) = 160000*a(n-1).
a(n) = A013777(n)*A013793(n) = A009964(A004767(n)). (End)

A013895 a(n) = 20^(5*n + 2).

Original entry on oeis.org

400, 1280000000, 4096000000000000, 13107200000000000000000, 41943040000000000000000000000, 134217728000000000000000000000000000, 429496729600000000000000000000000000000000, 1374389534720000000000000000000000000000000000000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (3200000).

Subsequence of A009964.

Cf. A013823, A013855, A013894, A013896, A016873.

[20^(5*n+2): n in [0..10]]; // Vincenzo Librandi, May 27 2011

A013895:=n->20^(5*n+2): seq(A013895(n), n=0..10); # Wesley Ivan Hurt, Nov 17 2015

20^(5 Range[0, 10] + 2) (* or *) CoefficientList[Series[-400/(3200000*x - 1), {x, 0, 10}], x] (* Wesley Ivan Hurt, Nov 17 2015 *)

Vec(-400/(3200000*x-1) + O(x^10)) \\ Colin Barker, Nov 17 2015

a(n) = 3200000*a(n-1), a(0)=400. - Vincenzo Librandi, May 27 2011
G.f.: -400/(3200000*x-1). - Colin Barker, Nov 17 2015
a(n) = A009964(A016873(n)). - Wesley Ivan Hurt, Nov 17 2015
From Elmo R. Oliveira, Jul 13 2025: (Start)
E.g.f.: 400*exp(3200000*x).
a(n) = 20*A013894(n) = A013896(n)/20 = A013823(n)*A013855(n). (End)

A013897 a(n) = 20^(5*n + 4).

Original entry on oeis.org

160000, 512000000000, 1638400000000000000, 5242880000000000000000000, 16777216000000000000000000000000, 53687091200000000000000000000000000000, 171798691840000000000000000000000000000000000, 549755813888000000000000000000000000000000000000000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..50
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (3200000).

Subsequence of A009964.

Cf. A013825, A013857, A016897.

[20^(5*n+4): n in [0..10]]; // Vincenzo Librandi, May 27 2011

20^(5*Range[0,10]+4) (* or *) NestList[3200000#&,160000,10] (* Harvey P. Dale, Feb 15 2016 *)

a(n) = 3200000*a(n-1), a(0)=160000. - Vincenzo Librandi, May 27 2011
From Elmo R. Oliveira, Jul 11 2025: (Start)
G.f.: 160000/(1-3200000*x).
E.g.f.: 160000*exp(3200000*x).
a(n) = A013825(n)*A013857(n) = A009964(A016897(n)). (End)

A156746 Numerator of Euler(n, 1/20).

Original entry on oeis.org

1, -9, -19, 1971, 7961, -1580049, -9560059, 2686469931, 21670511921, -7838281432089, -79034002960099, 34943616861129891, 422806632973239881, -220928651974538628129, -3118693689740162472139, 1880318896105818396109851, 30335009203988869812319841

Offset: 0

N. J. A. Sloane, Nov 07 2009

T. D. Noe, Table of n, a(n) for n = 0..100

For denominators see A009964.

Numerator[EulerE[Range[0,20],1/20]] (* Harvey P. Dale, Oct 13 2017 *)

G.f.: conjecture T(0)/(1+9*x), where T(k) = 1 - 100*x^2*(k+1)^2/(100*x^2*(k+1)^2 + (1+ 9*x)^2/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 12 2013

A156751 Numerator of Euler(n, 3/20).

Original entry on oeis.org

1, -7, -51, 1757, 23001, -1423807, -27733851, 2423221157, 62887847601, -7070927698807, -229364654629251, 31523048882011757, 1227032077593393801, -199302585894622665007, -9050801142483361006251, 1696260152956539473013557, 88035625059010432835381601

Offset: 0

N. J. A. Sloane, Nov 07 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..200

For denominators see A009964.

 Numerator[EulerE[Range[0,20],3/20]] (* Vincenzo Librandi, May 08 2012 *)

A156754 Numerator of Euler(n, 7/20).

Original entry on oeis.org

1, -3, -91, 873, 44681, -723243, -54370771, 1234258113, 123409465361, -3602675046483, -450147484965451, 16061724748579353, 2408182490139558041, -101549689784375097723, -17763194493523591880131, 864287669702052258292593, 172779639453348550866418721

Offset: 0

N. J. A. Sloane, Nov 07 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..200

For denominators see A009964.

 Numerator[EulerE[Range[0,20],7/20]] (* Vincenzo Librandi, May 08 2012 *)

A156757 Numerator of Euler(n, 9/20).

Original entry on oeis.org

1, -1, -99, 299, 49401, -249001, -60251499, 425252099, 136795497201, -1241382296401, -498990299504499, 5534485665505499, 2669489641160743401, -34991633084859742201, -19690651784477632959099, 297813229679687736760499, 191527704666360326602988001

Offset: 0

N. J. A. Sloane, Nov 07 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..200

For denominators see A009964.

Numerator[EulerE[Range[0,20],9/20]] (* Vincenzo Librandi, May 08 2012 *)

A165841 Totally multiplicative sequence with a(p) = 20.

Original entry on oeis.org

1, 20, 20, 400, 20, 400, 20, 8000, 400, 400, 20, 8000, 20, 400, 400, 160000, 20, 8000, 20, 8000, 400, 400, 20, 160000, 400, 400, 8000, 8000, 20, 8000, 20, 3200000, 400, 400, 400, 160000, 20, 400, 400, 160000, 20, 8000, 20, 8000, 8000, 400, 20, 3200000, 400

Offset: 1

Jaroslav Krizek, Sep 28 2009

G. C. Greubel, Table of n, a(n) for n = 1..10000

20^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 09 2016 *)

a(n) = A009964(A001222(n)) = 20^bigomega(n) = 20^A001222(n).

cp's OEIS Frontend

A013812 a(n) = 20^(4*n + 1).

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A013813 a(n) = 20^(4*n + 3).

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A013895 a(n) = 20^(5*n + 2).

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A013897 a(n) = 20^(5*n + 4).

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A156746 Numerator of Euler(n, 1/20).

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Mathematica

Formula

A156751 Numerator of Euler(n, 3/20).

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Mathematica

A156754 Numerator of Euler(n, 7/20).

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Mathematica

A156757 Numerator of Euler(n, 9/20).

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Mathematica

A165841 Totally multiplicative sequence with a(p) = 20.

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