A331689 E.g.f.: exp(x/(1 - x)) / (1 - 2*x).
1, 3, 15, 103, 897, 9471, 117703, 1685475, 27361953, 497111707, 10001175231, 220849928223, 5312868439585, 138337555830423, 3876986580776247, 116375171226474331, 3725295913465848513, 126686907674290095795, 4561317309742758852463, 173343622143918424951767
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..403
Programs
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Maple
b:= proc(n) b(n):= `if`(n<0, 0, 1+n*b(n-1)) end: a:= n-> n!*add(binomial(n, k)*b(k)/k!, k=0..n): seq(a(n), n=0..23); # Alois P. Heinz, Jan 24 2020
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Mathematica
nmax = 19; CoefficientList[Series[Exp[x/(1 - x)]/(1 - 2 x), {x, 0, nmax}], x] Range[0, nmax]! A000522[0] = 1; A000522[n_] := Floor[Exp[1] n!]; a[n_] := Sum[Binomial[n, k]^2 k! A000522[n - k], {k, 0, n}]; Table[a[n], {n, 0, 19}]
Formula
a(n) = Sum_{k=0..n} binomial(n,k)^2 * k! * A000522(n-k).
a(n) = Sum_{k=0..n} binomial(n,k) * k! * 2^k * A000262(n-k).
a(n) ~ n! * exp(1) * 2^n. - Vaclav Kotesovec, Jan 26 2020