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

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..403

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

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

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}]

Crossrefs

Cf. A000165, A000262, A000522, A002720, A010842, A010844, A331688.

Sequence in context: A372698 A343884 A358738 * A001274 A139766 A003276

Adjacent sequences: A331686 A331687 A331688 * A331690 A331691 A331692

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 24 2020

Status

approved