A001020 -id:A001020 - cp's OEIS frontend

A086874 Seventh power of odd primes.

2187, 78125, 823543, 19487171, 62748517, 410338673, 893871739, 3404825447, 17249876309, 27512614111, 94931877133, 194754273881, 271818611107, 506623120463, 1174711139837, 2488651484819, 3142742836021, 6060711605323

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Sep 16 2003

Cf. A000040, A001248, A030078, A030514, A050997, A030516, A000244, A000351, A000420, A001020, A001022, A001026, A001029, A009967, A009973, A009975, A009981, A009985, A009987, A009991.

Prime[Range[2,20]]^7 (* Harvey P. Dale, Sep 16 2013 *)

a(n) = prime(n+1)^7 \\ Michel Marcus, Jul 17 2013

A091947 (Fractional part of 1.1^n) * 10^n.

Original entry on oeis.org

0, 1, 21, 331, 4641, 61051, 771561, 9487171, 14358881, 357947691, 5937424601, 85311670611, 138428376721, 4522712143931, 79749833583241, 177248169415651, 5949729863572161, 5447028499293771, 559917313492231481

Offset: 0

Reinhard Zumkeller, Feb 16 2004

nonn

a(n) = A001020(n) mod A011557(n).

			a(2) = (1.1^2 - floor(1.1^2))*10^2 = (1.21 - 1)*100 = 21.

Eric Weisstein's World of Mathematics, Fractional Part

Cf. A091946.

Table[ FractionalPart[(11/10)^n] 10^n, {n, 0, 19}] (* Robert G. Wilson v, Feb 18 2004 *)

A094972 a(n) = floor(11^n/2^n).

Original entry on oeis.org

1, 5, 30, 166, 915, 5032, 27680, 152243, 837339, 4605366, 25329516, 139312339, 766217865, 4214198259, 23178090428, 127479497357, 701137235467, 3856254795069, 21209401372879, 116651707550839, 641584391529617

Offset: 0

Robert G. Wilson v, May 26 2004

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Cf. A000079, A001020.

Cf. A002379, A094969-A094999.

[Floor(11^n / 2^n): n in [0..30]]; // Vincenzo Librandi, Sep 08 2011

Mathematica
```
Table[ Floor[(11/2)^n], {n, 0, 30}]
```

A094972(n):=floor(11^n/2^n)$ makelist(A094972(n),n,0,60); /* Martin Ettl, Oct 25 2012 */

a(n)=11^n>>n \\ Charles R Greathouse IV, Feb 04 2016

A110195 a(n) = 11^((n^2-n)/2).

Original entry on oeis.org

1, 1, 11, 1331, 1771561, 25937424601, 4177248169415651, 7400249944258160101211, 144209936106499234037676064081, 30912680532870672635673352936887453361, 72890483685103052142902866787761839379440139451, 1890591424712781041871514584574319778449301246603238034051

Offset: 0

Philippe Deléham, Sep 07 2005

Sequence given by the Hankel transform (see A001906 for definition) of A082173 = {1, 1, 12, 155, 2124, 30482, 453432, 6936799, ...}; example : det([1, 1, 12, 155; 1, 12, 155, 2124; 12, 155, 2124, 30482; 155, 2124, 30482, 453432]) = 11^6 = 1771561.

Cf. A001020, A006125, A047656, A053763, A053764, A109345, A109354, A109493, A109966, A110147, A161680.

Table[11^((n^2-n)/2),{n,0,20}] (* Harvey P. Dale, Feb 02 2012 *)
Join[{1,1},Table[Det[Table[Binomial[11i,j],{i,n},{j,n}]],{n,10}]] (* Harvey P. Dale, Apr 01 2019 *)

a(n+1) is the determinant of n X n matrix M_(i, j) = binomial(11i, j).

a(n) = A001020(A161680(n)).

a(11) from Harvey P. Dale, Feb 02 2012

a(12) from Jason Yuen, Aug 29 2025

A139744 a(n) = 11^n - 6^n.

Original entry on oeis.org

0, 5, 85, 1115, 13345, 153275, 1724905, 19207235, 212679265, 2347869995, 25876958425, 284948873555, 3136251594385, 34509651449915, 379671469419145, 4176777984431075, 45946908753664705, 505430101839849035, 5559815753535563065, 61158481088674535795

Offset: 0

N. J. A. Sloane, May 20 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (17,-66).

Cf. A000400, A001020.

[11^n-6^n: n in [0..30]]; // Vincenzo Librandi, Jun 02 2011

Table[11^n-6^n,{n,0,30}] (* or *) LinearRecurrence[{17,-66},{0,5},30] (* Harvey P. Dale, Jul 17 2019 *)

a(n) = 17*a(n-1) - 66*a(n-2). Vincenzo Librandi, Jun 02 2011
From Stefano Spezia, Dec 17 2022: (Start)
O.g.f.: 5*x/((1 - 6*x)*(1 - 11*x)).
E.g.f.: exp(6*x)*(exp(5*x) - 1). (End)

A159460 Numerator of Hermite(n, 9/11).

Original entry on oeis.org

1, 18, 82, -7236, -189780, 3588408, 294225144, 85684176, -496875078768, -9109635982560, 918220473870624, 38573287607466432, -1749983724509205312, -143516534253248214144, 2922151180747492056960, 538832739303459806545152, -908419478651119648952064

Offset: 0

N. J. A. Sloane, Nov 12 2009

			Numerator of 1, 18/11, 82/121, -7236/1331, -189780/14641, 3588408/161051, ...

Vincenzo Librandi, Table of n, a(n) for n = 0..200
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Cf. A001020 (denominators).

[Numerator((&+[(-1)^k*Factorial(n)*(18/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 15 2018

A159460 := proc(n)
        orthopoly[H](n,9/11) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Numerator[Table[HermiteH[n,9/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)

a(n)=numerator(polhermite(n,9/11)) \\ Charles R Greathouse IV, Jan 29 2016

D-finite with recurrence a(n) - 18*a(n-1) + 242*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jun 15 2018: (Start)
a(n) = 11^n * Hermite(n,9/11).
E.g.f.: exp(18*x-121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(18/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159470 Numerator of Hermite(n, 10/11).

Original entry on oeis.org

1, 20, 158, -6520, -245108, 1409200, 324764680, 4449135200, -461168663920, -17836899025600, 647687369505760, 56119043032067200, -601762916982989120, -175004959304782931200, -1606953049267174852480, 560777741139261073856000, 17048794391625066191622400

Offset: 0

N. J. A. Sloane, Nov 12 2009

			Numerator of 1, 20/11, 158/121, -6520/1331, -245108/14641, 1409200/161051, ...

Vincenzo Librandi, Table of n, a(n) for n = 0..200
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Cf. A001020 (denominators).

[Numerator((&+[(-1)^k*Factorial(n)*(20/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 15 2018

A159470 := proc(n)
        orthopoly[H](n,10/11) ;
        numer(%) ;
end proc: # R. J. Mathar, Feb 16 2014

Numerator[Table[HermiteH[n,10/11],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)

a(n)=numerator(polhermite(n,10/11)) \\ Charles R Greathouse IV, Jan 29 2016

D-finite with recurrence a(n) - 20*a(n-1) + 242*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
From G. C. Greubel, Jun 15 2018: (Start)
a(n) = 11^n * Hermite(n,10/11).
E.g.f.: exp(20*x-121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159806 Numerator of Hermite(n, 1/22).

Original entry on oeis.org

1, 1, -241, -725, 174241, 876041, -209955569, -1481967101, 354182766785, 3223271074321, -768186794983409, -8568502794840229, 2036344745450994529, 26919276861667019545, -6379421292327161768689, -97581931299655023987149, 23059717359847942196353921

Offset: 0

N. J. A. Sloane, Nov 12 2009

			Numerator of 1, 1/11, -241/121, -725/1331, 174241/14641, ...

G. C. Greubel, Table of n, a(n) for n = 0..434

Cf. A001020 (denominators).

[Numerator((&+[(-1)^k*Factorial(n)*(1/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 21 2018

Numerator[Table[HermiteH[n, 1/22], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[11^n*HermiteH[n, 1/22], {n,0,50}] (* G. C. Greubel, Jul 11 2018 *)

a(n)=numerator(polhermite(n, 1/22)) \\ Charles R Greathouse IV, Jan 29 2016

From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 11^n * Hermite(n, 1/22).
E.g.f.: exp(x - 121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

A159807 Numerator of Hermite(n, 3/22).

Original entry on oeis.org

1, 3, -233, -2151, 162705, 2570283, -189162201, -4299537519, 307542155937, 9246531104595, -642087222317001, -24302866940070903, 1636327584987643953, 75484508348928834171, -4921433057324341373625, -270505813458143914292223, 17053284557712927443382081

Offset: 0

N. J. A. Sloane, Nov 12 2009

			Numerators of 1, 3/11, -233/121, -2151/1331, 162705/14641, ...

G. C. Greubel, Table of n, a(n) for n = 0..435
DLMF Digital library of mathematical functions, Table 18.9.1 for H_n(x)

Cf. A001020 (denominators).

[Numerator((&+[(-1)^k*Factorial(n)*(3/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 21 2018

Numerator/@HermiteH[Range[0,20],3/22]  (* Harvey P. Dale, May 01 2011 *)

makelist(num(hermite(n, 3/22)), n, 0, 20); /* Bruno Berselli, Jan 19 2017 */

a(n)=numerator(polhermite(n, 3/22)) \\ Charles R Greathouse IV, Jan 29 2016

[numerator(hermite(n, 3/22)) for n in range(20)] # Bruno Berselli, Jan 19 2017

From Vincenzo Librandi, Jan 20 2017: (Start)
Conjecture: E.g.f.: exp(-x*(121*x-3)).
D-finite with recurrence a(n) = 3*a(n-1) - 242*(n-1)*a(n-2). [DLMF] Corrected Feb 06 2021 (End)

A159808 Numerator of Hermite(n, 5/22).

Original entry on oeis.org

1, 5, -217, -3505, 140017, 4092925, -148955945, -6687706825, 218892836705, 14041864596725, -406539275359865, -36014008700873825, 902137507503591505, 109095368804855545325, -2292647754582021148105, -381078348283760693301625, 6416919607713933301113025

Offset: 0

N. J. A. Sloane, Nov 12 2009

			Numerators of 1, 5/11, -217/121, -3505/1331, 140017/14641, ...

G. C. Greubel, Table of n, a(n) for n = 0..434

Cf. A001020 (denominators).

[Numerator((&+[(-1)^k*Factorial(n)*(5/11)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, May 21 2018

Numerator[Table[HermiteH[n, 5/22], {n, 0, 30}]] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2011 *)
Table[11^n*HermiteH[n, 5/22], {n,0,30}] (* G. C. Greubel, Jul 11 2018 *)

a(n)=numerator(polhermite(n, 5/22)) \\ Charles R Greathouse IV, Jan 29 2016

From G. C. Greubel, Jul 11 2018: (Start)
a(n) = 11^n * Hermite(n, 5/22).
E.g.f.: exp(5*x - 121*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/11)^(n-2*k)/(k!*(n-2*k)!)). (End)

cp's OEIS Frontend

A086874 Seventh power of odd primes.

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A091947 (Fractional part of 1.1^n) * 10^n.

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A094972 a(n) = floor(11^n/2^n).

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Magma

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Maxima

PARI

A110195 a(n) = 11^((n^2-n)/2).

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Formula

Extensions

A139744 a(n) = 11^n - 6^n.

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Magma

Mathematica

Formula

A159460 Numerator of Hermite(n, 9/11).

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Magma

Maple

Mathematica

PARI

Formula

A159470 Numerator of Hermite(n, 10/11).

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Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A159806 Numerator of Hermite(n, 1/22).

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