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A335595 E.g.f.: exp(-x * (2 + x)) / (1 - x)^2. 1
1, 0, 0, 4, 12, 48, 400, 3120, 25872, 251776, 2715264, 31809600, 405296320, 5580385536, 82469607168, 1302102360832, 21875297337600, 389590168842240, 7331376554610688, 145352459953603584, 3028176414606560256, 66135374473635328000, 1510938930307368898560, 36038691473858577444864 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(0) = 1; a(n) = 2 * Sum_{k=3..n} binomial(n-1,k-1) * (k-1)! * a(n-k).

a(n) = Sum_{k=0..n} binomial(n,k) * Hermite(k,-1) * (n-k+1)!.

a(n) = Sum_{k=0..n} binomial(n,k) * A038205(k) * A038205(n-k).

a(n) ~ exp(-3) * n * n!. - Vaclav Kotesovec, Aug 09 2021

D-finite with recurrence a(n) +(-n+1)*a(n-1) -2*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Aug 20 2021

MAPLE

A335595 := proc(n)

    option remember ;

    if n = 0 then

        1;

    else

        2*add(binomial(n-1, k-1)*(k-1)!*procname(n-k), k=3..n) ;

    end if;

end proc:

seq(A335595(n), n=0..42) ; # R. J. Mathar, Aug 20 2021

MATHEMATICA

nmax = 23; CoefficientList[Series[Exp[-x (2 + x)]/(1 - x)^2, {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n - 1, k - 1] (k - 1)! a[n - k], {k, 3, n}]; Table[a[n], {n, 0, 23}]

Table[Sum[Binomial[n, k] HermiteH[k, -1] (n - k + 1)!, {k, 0, n}], {n, 0, 23}]

PROG

(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(-x*(2+x))/(1-x)^2)) \\ Michel Marcus, Nov 21 2020

CROSSREFS

Cf. A038205, A087981.

Sequence in context: A192622 A324801 A111930 * A197867 A013935 A149386

Adjacent sequences:  A335592 A335593 A335594 * A335596 A335597 A335598

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 20 2020

STATUS

approved

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Last modified October 21 18:51 EDT 2021. Contains 348155 sequences. (Running on oeis4.)