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.

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A302686 a(n) = [x^n] 1 + x*(1 + x*(1 + x*(1 + x*(1 + ...)^(4*n))^(3*n))^(2*n))^n.

Original entry on oeis.org

1, 1, 2, 21, 596, 32805, 2960496, 396523540, 73803150440, 18216533196693, 5757491981210470, 2267526164705341925, 1088820552191787545688, 626169526288460672060244, 424903177461959840892846066, 335946105815409394263421836000, 306145042287138023678922165314512
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 11 2018

Keywords

Crossrefs

Cf. A095793, A138212, A138213, A138214, A138215, A138216, A302657.

Programs

  • Mathematica
    Table[SeriesCoefficient[1 + x Fold[(x #1 + 1)^(n #2) &, 0, Reverse[Range[n]]], {x, 0, n}], {n, 0, 16}]

A302688 Expansion of 1 + x*(1 + 2*x*(1 + 3*x*(1 + 4*x*(1 + 5*x*(1 + ...)^5)^4)^3)^2).

Original entry on oeis.org

1, 1, 2, 12, 162, 3888, 144768, 7693920, 551981520, 51355426992, 6010929609408, 864202875949440, 149698423474606080, 30747550680449611200, 7388611598645058636000, 2053517715502048081023360, 653614372412684344833419520, 236202930442590804658824312960
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 11 2018

Keywords

Comments

(a(n) / n!^2)^(1/n) tends to 1.36594... - Vaclav Kotesovec, Apr 12 2018

Links

Crossrefs

Cf. A095793, A128318, A128319, A138211, A138212.

Programs

  • Mathematica
    nmax = 17; CoefficientList[Series[1 + x Fold[((#2 + 1) x #1 + 1)^#2 &, 0, Reverse[Range[nmax]]], {x, 0, nmax}], x]

Formula

G.f. A(x) = 1 + x + 2*x^2 + 12*x^3 + 162*x^4 + 3888*x^5 + 144768*x^6 + 7693920*x^7 + 551981520*x^8 + ...

A302751 Expansion of 1 + x*(1 + 2*x^2*(1 + 3*x^3*(1 + 4*x^4*(1 + ...)^4)^3)^2).

Original entry on oeis.org

1, 1, 0, 2, 0, 0, 12, 0, 0, 18, 144, 0, 0, 432, 576, 2880, 0, 4320, 9408, 23040, 21600, 109440, 172800, 110880, 662400, 832320, 2678400, 4060800, 10296000, 9412992, 32922000, 63676800, 135734400, 263556528, 281030400, 973036800, 1906704000, 4069224000, 5184984960
Offset: 0

Views

Author

Ilya Gutkovskiy, Apr 12 2018

Keywords

Examples

			G.f. A(x) = 1 + x + 2*x^3 + 12*x^6 + 18*x^9 + 144*x^10 + 432*x^13 + 576*x^14 + 2880*x^15 + ...

Crossrefs

Cf. A095793, A108643, A128318, A228866, A302688.

Programs

  • Mathematica
    nmax = 38; CoefficientList[Series[1 + x Fold[((#2 + 1) x^(#2 + 1) #1 + 1)^#2 &, 0, Reverse[Range[nmax]]], {x, 0, nmax}], x]
Previous Showing 11-13 of 13 results.

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

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