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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A381480 E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x) * cos(x * A(x)) )^2.

Original entry on oeis.org

1, 2, 14, 174, 3168, 76450, 2304720, 83473726, 3533382272, 171254814210, 9355068840960, 568799458870478, 38102773549750272, 2788540163472852386, 221380225364522119168, 18950242574522637197790, 1739955233454599038402560, 170582215179135413189856514, 17785491645892269582026145792
Offset: 0

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Author

Seiichi Manyama, Feb 24 2025

Keywords

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Crossrefs

Cf. A185951, A381478.

Programs

  • PARI
    a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = 2*sum(k=0, n, k!*binomial(2*n+k+2, k)/(2*n+k+2)*I^(n-k)*a185951(n, k));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A381479.
a(n) = 2 * Sum_{k=0..n} k! * binomial(2*n+k+2,k)/(2*n+k+2) * i^(n-k) * A185951(n,k), where i is the imaginary unit.
E.g.f.: (1/x) * Series_Reversion( x*(1 - x*cos(x))^2 ).
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