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 1-4 of 4 results.

A196665 Expansion of g.f. (1-6*x)/(1-19*x).

Original entry on oeis.org

1, 13, 247, 4693, 89167, 1694173, 32189287, 611596453, 11620332607, 220786319533, 4194940071127, 79703861351413, 1514373365676847, 28773093947860093, 546688785009341767, 10387086915177493573, 197354651388372377887, 3749738376379075179853
Offset: 0

Views

Author

Philippe Deléham, Oct 05 2011

Keywords

Links

Crossrefs

Cf. A002001, A193722, A196661, A196662, A196663, A196664.

Formula

a(0) = 1, a(n) = 13*19^(n-1) for n>0.
a(n) = Sum_{k=0..n} A193722(n,k)*6^k.
From Elmo R. Oliveira, Mar 18 2025: (Start)
E.g.f.: (13*exp(19*x) + 6)/19.
a(n) = 19*a(n-1) for n > 1. (End)

A196666 Expansion of g.f. (1 - 7*x)/(1 - 22*x).

Original entry on oeis.org

1, 15, 330, 7260, 159720, 3513840, 77304480, 1700698560, 37415368320, 823138103040, 18109038266880, 398398841871360, 8764774521169920, 192825039465738240, 4242150868246241280, 93327319101417308160, 2053201020231180779520, 45170422445085977149440
Offset: 0

Views

Author

Philippe Deléham, Oct 05 2011

Keywords

Links

Crossrefs

Cf. A002001, A193722, A196661, A196662, A196663, A196664, A196665.

Programs

Formula

a(0) = 1, a(n) = 15*22^(n-1) for n>0.
a(n) = Sum_{k=0..n} A193722(n,k)*7^k.
From Elmo R. Oliveira, Mar 25 2025: (Start)
E.g.f.: (15*exp(22*x) + 7)/22.
a(n) = 22*a(n-1) for n > 1. (End)

A196512 Expansion of g.f. (1-9*x)/(1-28*x).

Original entry on oeis.org

1, 19, 532, 14896, 417088, 11678464, 326996992, 9155915776, 256365641728, 7178237968384, 200990663114752, 5627738567213056, 157576679881965568, 4412147036695035904, 123540117027461005312, 3459123276768908148736, 96855451749529428164608, 2711952648986823988609024
Offset: 0

Views

Author

Philippe Deléham, Oct 05 2011

Keywords

Links

Crossrefs

Cf. A002001, A193722, A196661, A196662, A196663, A196664, A196665, A196666, A196676.

Programs

Formula

a(n) = 19*28^(n-1) for n > 0, a(0)=1.
a(n) = Sum_{k=0..n} A193722(n,k)*9^k.
From Elmo R. Oliveira, Mar 25 2025: (Start)
E.g.f.: (19*exp(28*x) + 9)/28.
a(n) = 28*a(n-1) for n > 1. (End)

A196676 Expansion of g.f. (1-8*x)/(1-25*x).

Original entry on oeis.org

1, 17, 425, 10625, 265625, 6640625, 166015625, 4150390625, 103759765625, 2593994140625, 64849853515625, 1621246337890625, 40531158447265625, 1013278961181640625, 25331974029541015625, 633299350738525390625, 15832483768463134765625, 395812094211578369140625, 9895302355289459228515625
Offset: 0

Views

Author

Philippe Deléham, Oct 05 2011

Keywords

Links

Crossrefs

Cf. A002001, A193722, A196661, A196662, A196663, A196664, A196665, A196666.

Programs

  • Mathematica
    CoefficientList[Series[(1-8x)/(1-25x),{x,0,30}],x] (* Harvey P. Dale, Apr 29 2014 *)

Formula

a(0) = 1, a(n) = 17*25^(n-1) for n>0.
a(n) = Sum_{k=0..n} A193722(n,k)*8^k.
From Elmo R. Oliveira, Mar 25 2025: (Start)
E.g.f.: (17*exp(25*x) + 8)/25.
a(n) = 25*a(n-1) for n > 1. (End)

Extensions

More terms from Elmo R. Oliveira, Mar 25 2025
Showing 1-4 of 4 results.

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

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