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A121020 Lah transform of A104600. 1

%I #13 Apr 04 2020 10:30:06

%S 1,1,7,85,1587,41981,1484643,67306429,3790883659,258899180989,

%T 21029065282803,1999625128004813,219691693064750283,

%U 27580289062408474861,3919060527556589637043,625165018565884343909053

%N Lah transform of A104600.

%H Jean-François Alcover, <a href="/A121020/b121020.txt">Table of n, a(n) for n = 0..80</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F 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.

%p 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

%t 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}];

%t Reap[For[n = 0, n <= 80, n++, Print[n, " ", a[n]]; Sow[a[n]]]][[2, 1]] (* _Jean-François Alcover_, Apr 04 2020 *)

%K easy,nonn

%O 0,3

%A _Vladeta Jovovic_, Sep 08 2006, Sep 19 2006

%E More terms from _R. J. Mathar_, Jan 21 2008

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Last modified March 29 06:34 EDT 2024. Contains 371265 sequences. (Running on oeis4.)