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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A344419 a(n) = n*a(n-1) + n^(n mod 2), a(0) = 0.

Original entry on oeis.org

0, 1, 3, 12, 49, 250, 1501, 10514, 84113, 757026, 7570261, 83272882, 999274585, 12990569618, 181867974653, 2728019619810, 43648313916961, 742021336588354, 13356384058590373, 253771297113217106, 5075425942264342121, 106583944787551184562, 2344846785326126060365
Offset: 0

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Author

Alois P. Heinz, May 17 2021

Keywords

Crossrefs

Programs

  • Maple
    a:= proc(n) a(n):= n*a(n-1) + n^(n mod 2) end: a(0):= 0:
    seq(a(n), n=0..23);

Formula

E.g.f.: ((x+1)*cosh(x)-1)/(1-x).
a(n) = A344262(n) - n! = A344262(n) - A000142(n).
a(n) = A344418(n) - A155521(n-1) for n > 0.
Lim_{n->infinity} a(n)/n! = 2*cosh(1)-1 = 2*A073743-1 = e+1/e-1 = A137204-1. - Amrit Awasthi, May 20 2021
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