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.

A301627 G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x)/(1 - x^2*A(x)^2/(1 - x^3*A(x)^3/(1 - x^4*A(x)^4/(1 - ...))))), a continued fraction.

Original entry on oeis.org

1, 1, 2, 6, 20, 71, 265, 1024, 4059, 16414, 67451, 280856, 1182379, 5024361, 21522055, 92833874, 402879747, 1757852317, 7706728006, 33932931008, 149986338830, 665276977574, 2960306454110, 13210976195068, 59114318997648, 265166069469324, 1192145264317628, 5370983954821322
Offset: 0

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Author

Ilya Gutkovskiy, Mar 24 2018

Keywords

Examples

			G.f. A(x) = 1 + x + 2*x^2 + 6*x^3 + 20*x^4 + 71*x^5 + 265*x^6 + 1024*x^7 + 4059*x^8 + 16414*x^9 + 67451*x^10 + ...
log(A(x)) = x + 3*x^2/2 + 13*x^3/3 + 55*x^4/4 + 236*x^5/5 + 1035*x^6/6 + 4593*x^7/7 + 20551*x^8/8 + ... + A291653(n)*x^n/n + ...
		

Crossrefs

Formula

a(n) ~ c * d^n / n^(3/2), where d = 4.760595370947474723688065553003203505424287110594102605580439495640678... and c = 0.395762805862214496152624315213041270339036... - Vaclav Kotesovec, Apr 08 2018

A301629 G.f. A(x) satisfies: A(x) = 1/(1 + x*A(x)/(1 + x^2*A(x)^2/(1 + x^3*A(x)^3/(1 + x^4*A(x)^4/(1 + ...))))), a continued fraction.

Original entry on oeis.org

1, -1, 2, -4, 8, -15, 23, -14, -95, 616, -2597, 9280, -29971, 89283, -245617, 614122, -1330205, 2121789, -134318, -18870272, 111955244, -481559262, 1783749762, -5976975892, 18406561660, -52025500982, 132347403714, -285820317372, 421120353772, 271625450178, -5772145145591
Offset: 0

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Author

Ilya Gutkovskiy, Mar 24 2018

Keywords

Examples

			G.f. A(x) = 1 - x + 2*x^2 - 4*x^3 + 8*x^4 - 15*x^5 + 23*x^6 - 14*x^7 - 95*x^8 + 616*x^9 - 2597*x^10 + ...
log(A(x)) = -x + 3*x^2/2 - 7*x^3/3 + 15*x^4/4 - 26*x^5/5 + 15*x^6/6 + 153*x^7/7 - 1049*x^8/8 + ... + A291651(n)*x^n/n + ...
		

Crossrefs

A301411 G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x) - x*A(x)^2/(1 - x*A(x)^3 - x*A(x)^4/(1 - x*A(x)^5 - x*A(x)^6/(1 - ...)))), a continued fraction.

Original entry on oeis.org

1, 2, 12, 108, 1192, 14848, 200432, 2866752, 42853392, 663565616, 10579117744, 172911177584, 2888445810864, 49203276384624, 853289008064304, 15047071017842928, 269585532569464752, 4904425594952671344, 90570287337341726256, 1697589267552262891760, 32295562088556275945136
Offset: 0

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Author

Ilya Gutkovskiy, Mar 20 2018

Keywords

Examples

			G.f. A(x) = 1 + 2*x + 12*x^2 + 108*x^3 + 1192*x^4 + 14848*x^5 + 200432*x^6 + 2866752*x^7 + 42853392*x^8 + ...
		

Crossrefs

A301418 G.f. A(x) satisfies: A(x) = 1/(1 - x*A(x)/(1 - x*A(x)/(1 - x*A(x)^2/(1 - x*A(x)^2/(1 - x*A(x)^3/(1 - x*A(x)^3/(1 - ...))))))), a continued fraction.

Original entry on oeis.org

1, 1, 3, 12, 56, 288, 1584, 9153, 54940, 339937, 2156457, 13970079, 92147905, 617468715, 4195848863, 28873188732, 200982289554, 1413914236788, 10045715705912, 72041560145703, 521233406146366, 3803409400869139, 27982484503275869, 207531162828185908, 1551323994123301229
Offset: 0

Views

Author

Ilya Gutkovskiy, Mar 20 2018

Keywords

Examples

			G.f. A(x) = 1 + x + 3*x^2 + 12*x^3 + 56*x^4 + 288*x^5 + 1584*x^6 + 9153*x^7 + 54940*x^8 + ...
		

Crossrefs

Showing 1-4 of 4 results.