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 1-2 of 2 results.

A317904 Decimal expansion of a constant related to the asymptotics of A302598.

Original entry on oeis.org

3, 9, 5, 6, 1, 8, 4, 2, 0, 3, 0, 2, 6, 1, 6, 9, 7, 5, 4, 5, 4, 0, 8, 0, 2, 1, 8, 1, 8, 7, 8, 3, 0, 0, 8, 3, 3, 2, 9, 9, 9, 9, 8, 8, 0, 9, 5, 2, 5, 5, 5, 4, 0, 9, 8, 1, 6, 4, 9, 6, 2, 1, 1, 3, 0, 9, 3, 2, 8, 8, 5, 1, 3, 1, 4, 6, 2, 5, 2, 1, 2, 3, 0, 3, 1, 1, 5, 8, 9, 4, 8, 8, 4, 1, 6, 4, 0, 9, 6, 0, 7, 4, 7, 6, 5
Offset: 1

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Author

Vaclav Kotesovec, Aug 10 2018

Keywords

Examples

			3.9561842030261697545408021818783008332999988095...
		

Crossrefs

A323313 G.f. A(x) satisfies: 1 = Sum_{n>=0} ((1+x)^n - 1)^n/(A(x) + 1 - (1+x)^n)^(n+1).

Original entry on oeis.org

1, 1, 5, 42, 553, 9757, 213989, 5577285, 167819725, 5715066723, 217100774130, 9097820151376, 416870148834739, 20734141087348929, 1112567525238708108, 64067000804518722936, 3941130502347547574782, 257950869129924123671281, 17899157911139617070534480, 1312572773247815201019870104, 101429898156047011931583837037, 8238300763728888616466106146271, 701648737726537575830481016280283
Offset: 0

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Author

Paul D. Hanna, Feb 02 2019

Keywords

Examples

			G.f.: A(x) = 1 + x + 5*x^2 + 42*x^3 + 553*x^4 + 9757*x^5 + 213989*x^6 + 5577285*x^7 + 167819725*x^8 + 5715066723*x^9 + 217100774130*x^10 + ...
such that
1 = 1/A(x) + ((1+x) - 1)/(A(x) + 1 - (1+x))^2  +  ((1+x)^2 - 1)^2/(A(x) + 1 - (1+x)^2)^3  +  ((1+x)^3 - 1)^3/(A(x) + 1 - (1+x)^3)^4  +  ((1+x)^4 - 1)^4/(A(x) + 1 - (1+x)^4)^5  +  ((1+x)^5 - 1)^5/(A(x) + 1 - (1+x)^5)^6 + ...
also,
1 = 1/(A(x) + 2)  +  (1 + (1+x))/(A(x) + 1 + (1+x))^2  +  (1 + (1+x)^2)^2/(A(x) + 1 + (1+x)^2)^3  +  (1 + (1+x)^3)^3/(A(x) + 1 + (1+x)^3)^4  +  (1 + (1+x)^4)^4/(A(x) + 1 + (1+x)^4)^5  +  (1 + (1+x)^5)^5/(A(x) + 1 + (1+x)^5)^6 + ...
		

Crossrefs

Programs

  • PARI
    {a(n) = my(A=[1],X=x+x*O(x^n)); for(i=1,n, A=concat(A,0); A[#A] = Vec( sum(m=0, #A, ((1+X)^m - 1)^m / (Ser(A) + 1 - (1+X)^m)^(m+1) ) )[#A]); A[n+1]}
    for(n=0,30,print1(a(n),", "))

Formula

G.f. A(x) satisfies:
(1) 1 = Sum_{n>=0} ((1+x)^n - 1)^n/(A(x) + 1 - (1+x)^n)^(n+1).
(2) 1 = Sum_{n>=0} ((1+x)^n + 1)^n/(A(x) + 1 + (1+x)^n)^(n+1).
a(n) ~ c * A317904^n * n^n / exp(n), where c = 0.546536986945124389069... - Vaclav Kotesovec, Aug 11 2021
Showing 1-2 of 2 results.