A121020 Lah transform of A104600.

1, 1, 7, 85, 1587, 41981, 1484643, 67306429, 3790883659, 258899180989, 21029065282803, 1999625128004813, 219691693064750283, 27580289062408474861, 3919060527556589637043, 625165018565884343909053

Offset: 0

Author

Vladeta Jovovic, Sep 08 2006, Sep 19 2006

Keywords

• easy
• nonn

Links

• Jean-François Alcover, Table of n, a(n) for n = 0..80
• N. J. A. Sloane, Transforms

Programs

Maple

read "transforms" ; A000670 := proc(n) local k ; if n = 0 then 1; else add(k!*combinat[stirling2](n,k),k=1..n) ; fi ; end: A000110 := proc(n) local k ; add(combinat[stirling2](n,k),k=0..n) ; end: A104600 := proc(n) local k ; add(combinat[stirling1](n,k)*A000670(k)*A000110(k),k=0..n) ; end: A121020 := proc(nmax) local a104600 ; a104600 := [seq(A104600(n),n=0..nmax)] ; LAH(a104600) ; end: A121020(20) ; # R. J. Mathar, Jan 21 2008

Mathematica

a[n_] := a[n] = (1/(2 E)) Sum[Sum[Product[r s + k, {k, 0, n - 1}]/(2^r s!), {r, 0, Infinity}], {s, 0, Infinity}];
Reap[For[n = 0, n <= 80, n++, Print[n, " ", a[n]]; Sow[a[n]]]][[2, 1]] (* Jean-François Alcover, Apr 04 2020 *)

Formula

a(n) = 1/(2*exp(1))*Sum_{r,s>=0} [r*s]^n/(2^r*s!), where [m]^n = m*(m+1)*...*(m+n-1) is the rising factorial.

Extensions

More terms from R. J. Mathar, Jan 21 2008