A331658 E.g.f.: exp(x/(1 - 2*x)) / (1 - x).

1, 2, 9, 64, 617, 7446, 107377, 1795844, 34114929, 724822282, 17018900921, 437402060712, 12208463140249, 367629791490014, 11876750557295457, 409663873470828076, 15023747377122799457, 583644746007467984274, 23939828792355240206569, 1033788018952899566018192

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} binomial(n,k)^2 * k! * A000262(n-k).

a(n) = Sum_{k=0..n} binomial(n,k) * k! * A025168(n-k).

a(n) ~ 2^(n + 1/4) * n^(n - 1/4) * exp(-1/4 + sqrt(2*n) - n) * (1 - 23*sqrt(2) / (48*sqrt(n))). - Vaclav Kotesovec, Jan 26 2020

Mathematica

nmax = 19; CoefficientList[Series[Exp[x/(1 - 2 x)]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
A000262[n_] := If[n == 0, 1, n! Sum[Binomial[n - 1, k]/(k + 1)!, {k, 0, n - 1}]]; a[n_] := Sum[Binomial[n, k]^2 k! A000262[n - k], {k, 0, n}]; Table[a[n], {n, 0, 19}]

Crossrefs

Cf. A000262, A002720, A025167, A025168.

Sequence in context: A269577 A268104 A269683 * A269487 A179199 A036775

Adjacent sequences: A331655 A331656 A331657 * A331659 A331660 A331661

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 24 2020

Status

approved