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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A326983 Coefficients in asymptotic expansion of sequence A309618.

Original entry on oeis.org

1, 0, 2, 2, 10, 50, 250, 1442, 9514, 68882, 539098, 4546562, 41123338, 396400754, 4050377146, 43694283362, 495985850602, 5906224845266, 73578420729754, 956597103241922, 12951012525806026, 182233188537332018, 2660301596873941882, 40226477151229612322
Offset: 0

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Author

Vaclav Kotesovec, Aug 10 2019

Keywords

Examples

			A309618(n) / n! ~ 1 + 2/n^2 + 2/n^3 + 10/n^4 + 50/n^5 + 250/n^6 + ...
		

Crossrefs

Cf. A309618.

A309619 a(n) = Sum_{k=0..floor(n/2)} k! * (n - 2*k)!.

Original entry on oeis.org

1, 1, 3, 7, 28, 128, 754, 5178, 41124, 368220, 3670872, 40290744, 482716896, 6267697920, 87664818960, 1313983544400, 21010949076960, 357007805477280, 6423473819220480, 122003441554176000, 2439346762501367040, 51213306647556506880, 1126446562222595147520
Offset: 0

Views

Author

Vaclav Kotesovec, Aug 10 2019

Keywords

Crossrefs

Programs

  • Mathematica
    nmax = 25; CoefficientList[Series[Sum[k!*x^k, {k, 0, nmax}]*Sum[k!*x^(2*k), {k, 0, nmax}], {x, 0, nmax}], x]
    Table[Sum[k!*(n-2*k)!, {k, 0, Floor[n/2]}], {n, 0, 25}]
  • PARI
    a(n) = sum(k=0, n\2, k! * (n - 2*k)!); \\ Michel Marcus, Dec 08 2020

Formula

G.f.: B(x)*B(x^2), where B(x) is g.f. of A000142.
a(n) ~ n! * (1 + 1/n^2 + 1/n^3 + 3/n^4 + 13/n^5 + 57/n^6 + 271/n^7 + 1467/n^8 + 8905/n^9 + 58965/n^10 + ...), for coefficients see A326984.
Showing 1-2 of 2 results.