cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

A067427 Seventh column of triangle A067425.

Original entry on oeis.org

1, 10, 280, 7840, 219520, 6146560, 172103680, 4818903040, 134929285120, 3778019983360, 105784559534080, 2961967666954240, 82935094674718720, 2322182650892124160, 65021114224979476480, 1820591198299425341440
Offset: 0

Views

Author

Wolfdieter Lang, Jan 25 2002

Keywords

Links

Crossrefs

Cf. A067426 (sixth column), A067428 (eighth column), A009972 (powers of 28).

Programs

  • Magma
    [Ceiling(10*(4*7)^(n-1)): n in [0..20]]; // Vincenzo Librandi, Oct 03 2011
  • Mathematica
    LinearRecurrence[{28}, {1, 10}, 20] (* Paolo Xausa, Oct 16 2024 *)

Formula

a(n) = A067425(n+6, 6).
a(n) = 10*(4*7)^(n-1), n >= 1, a(0)=1.
G.f.: (1-18*x)/(1-28*x).

A218731 a(n) = (28^n - 1)/27.

Original entry on oeis.org

0, 1, 29, 813, 22765, 637421, 17847789, 499738093, 13992666605, 391794664941, 10970250618349, 307167017313773, 8600676484785645, 240818941573998061, 6742930364071945709, 188802050194014479853, 5286457405432405435885, 148020807352107352204781, 4144582605859005861733869
Offset: 0

Views

Author

M. F. Hasler, Nov 04 2012

Keywords

Comments

Partial sums of powers of 28 (A009972).

Links

Crossrefs

Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.
Cf. A009972.

Programs

Formula

From Vincenzo Librandi, Nov 07 2012: (Start)
G.f.: x/((1-x)*(1-28*x)).
a(n) = floor(28^n/27).
a(n) = 29*a(n-1) - 28*a(n-2). (End)
E.g.f.: exp(x)*(exp(27*x) - 1)/27. - Elmo R. Oliveira, Aug 29 2024

A157206 Numerator of Euler(n, 1/28).

Original entry on oeis.org

1, -13, -27, 5447, 21897, -8550373, -51521427, 28491956207, 228898201617, -162934942038973, -1636222143855627, 1423695084746914967, 17156395293052656537, -17642381532358409441173, -248035037340684934103427, 294301682652158427497809727
Offset: 0

Views

Author

N. J. A. Sloane, Nov 07 2009

Keywords

Links

Crossrefs

For denominators see A009972.

Programs

  • Mathematica
    Numerator[EulerE[Range[0,20],1/28]] (* Harvey P. Dale, Jul 29 2014 *)

A157232 Numerator of Euler(n, 3/28).

Original entry on oeis.org

1, -11, -75, 5137, 64425, -8116691, -151949475, 27061582537, 675202758225, -154763675249051, -4826608715002875, 1352304080132324737, 50608880246719532025, -16757717498380017159011, -731667579810789300424275, 279544164877458293190983737, 13948943072618103594908145825
Offset: 0

Views

Author

N. J. A. Sloane, Nov 07 2009

Keywords

Links

Crossrefs

For denominators see A009972.

Programs

  • Maple
    seq(numer(euler(n,3/28)),n=0..50); # Robert Israel, Jan 07 2019
  • Mathematica
    EulerE[Range[0,20],3/28]//Numerator (* Harvey P. Dale, Nov 06 2022 *)

Formula

E.g.f.: 2*exp(3*x)/(1+exp(28*x)). - Robert Israel, Jan 07 2019

A165849 Totally multiplicative sequence with a(p) = 28.

Original entry on oeis.org

1, 28, 28, 784, 28, 784, 28, 21952, 784, 784, 28, 21952, 28, 784, 784, 614656, 28, 21952, 28, 21952, 784, 784, 28, 614656, 784, 784, 21952, 21952, 28, 21952, 28, 17210368, 784, 784, 784, 614656, 28, 784, 784, 614656, 28, 21952, 28, 21952, 21952
Offset: 1

Views

Author

Jaroslav Krizek, Sep 28 2009

Keywords

Links

Programs

  • Mathematica
    28^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 13 2016 *)

Formula

a(n) = A009972(A001222(n)) = 28^bigomega(n) = 28^A001222(n).

A091480 Table of multigraphs (by antidiagonals) with n (>=1) nodes and k (>=0) edges. Each type of object labeled from its own label set.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 3, 1, 0, 1, 9, 6, 1, 0, 1, 27, 36, 10, 1, 0, 1, 81, 216, 100, 15, 1, 0, 1, 243, 1296, 1000, 225, 21, 1, 0, 1, 729, 7776, 10000, 3375, 441, 28, 1, 0, 1, 2187, 46656, 100000, 50625, 9261, 784, 36, 1, 0, 1, 6561, 279936, 1000000, 759375
Offset: 1

Views

Author

Christian G. Bower, Jan 13 2004

Keywords

Examples

			1  0   0    0     0 ...
1  1   1    1     1 ...
1  3   9   27    81 ...
1  6  36  216  1296 ...
1 10 100 1000 10000 ...

References

  • F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 114 (2.4.44).

Crossrefs

Columns 0-8: A000012, A000217(n-1), A000537(n-1), A059827(n-1), A059977(n-1), A059860(n-1), A059978(n-1), A059979(n-1), A059980(n-1).
Rows 1-10: A000007, A000012, A000244, A000400, A011557, A001024, A009965, A009972, A009980, A009989.
Cf. A091478.

Formula

a(n, k) = binomial(n, 2)^k.

A157233 Numerator of Euler(n, 5/28).

Original entry on oeis.org

1, -9, -115, 4563, 103385, -7273809, -244682395, 24273348363, 1087614676145, -138831344004249, -7774941663643075, 1213102349164829763, 81523593055504608905, -15032750772611708561889, -1178611204087999571493355, 250769133987648650402960763, 22469741388306099177659661665
Offset: 0

Views

Author

N. J. A. Sloane, Nov 07 2009

Keywords

Crossrefs

For denominators see A009972.

A157234 Numerator of Euler(n, 9/28).

Original entry on oeis.org

1, -5, -171, 2815, 163305, -4560125, -389093571, 15247993735, 1730774795985, -87230967310325, -12373627121809371, 762240242336496655, 129743913678787540665, -9445699930131209919725, -1875748758904668008579571, 157568683906141461793511575, 35760388081788065845786749345
Offset: 0

Views

Author

N. J. A. Sloane, Nov 07 2009

Keywords

Crossrefs

For denominators see A009972.

A157236 Numerator of Euler(n, 11/28).

Original entry on oeis.org

1, -3, -187, 1737, 181577, -2828523, -433608307, 9464818017, 1929308914577, -54151301196243, -13793410821936427, 473188884804949497, 144631586163051804377, -5863775132075093720763, -2090985354124427263262947, 97816726792847265070764177, 39863788048903869672547506977
Offset: 0

Views

Author

N. J. A. Sloane, Nov 07 2009

Keywords

Crossrefs

For denominators see A009972.

Programs

  • Mathematica
    Numerator[EulerE[Range[0,30],11/28]] (* Harvey P. Dale, Jan 29 2012 *)

A157239 Numerator of Euler(n, 13/28).

Original entry on oeis.org

1, -1, -195, 587, 190905, -958441, -456423435, 3208393187, 2031120835185, -18357153435601, -14521552284155475, 160410736104452987, 152266846748812455465, -1987817374606532447161, -2201371244223771530940315, 33159832798775207321651987, 41968251293767181816904683745
Offset: 0

Views

Author

N. J. A. Sloane, Nov 07 2009

Keywords

Crossrefs

For denominators see A009972.
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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