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.

A307604 G.f. A(x) satisfies: A(x) = (1/(1 - x)) * A(x^2)^2*A(x^3)^3*A(x^4)^4* ... *A(x^k)^k* ...

Original entry on oeis.org

1, 1, 3, 6, 17, 28, 72, 122, 282, 493, 1027, 1790, 3673, 6300, 12205, 21117, 39782, 67989, 124937, 212189, 381705, 644625, 1136315, 1905352, 3312916, 5513005, 9443362, 15624026, 26445046, 43451200, 72751824, 118792691, 196966722, 319714816, 525316191, 847734183, 1381904765
Offset: 0

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Author

Ilya Gutkovskiy, Apr 18 2019

Keywords

Comments

Euler transform of A050369.

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 6*x^3 + 17*x^4 + 28*x^5 + 72*x^6 + 122*x^7 + 282*x^8 + 493*x^9 + ...
		

Crossrefs

Programs

  • Mathematica
    terms = 36; A[] = 1; Do[A[x] = 1/(1 - x) Product[A[x^k]^k, {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

Formula

G.f.: Product_{k>=1} 1/(1 - x^k)^(k*A074206(k)).
a(n) ~ (-Gamma(2+r) * zeta(2+r) / zeta'(r))^(1/(50*(2+r))) * exp(12/625 + ((2+r)/(1+r)) * (-Gamma(2+r) * zeta(2+r) / zeta'(r))^(1/(2+r)) * n^((1+r)/(2+r))) / (A^(144/625) * sqrt(2*Pi*(2+r)) * n^(1/2 + 1/(50*(2+r)))), where r = A107311 is the root of the equation zeta(r)=2 and A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Mar 18 2021