A259455 - OEIS

%I #15 Jul 04 2015 20:49:28

%S 1,30,270,1400,5250,15876,41160,95040,200475,393250,726726,1277640,

%T 2153060,3498600,5508000,8434176,12601845,18421830,26407150,37191000,

%U 51546726,70409900,94902600,126360000,166359375,216751626,279695430,357694120,453635400,570834000

%N n Sum_n Sum_n Sum_n.

%C See the reference for an explanation of the rather cryptic definition.

%H Alois P. Heinz, <a href="/A259455/b259455.txt">Table of n, a(n) for n = 1..1000</a>

%H C. Krishnamachari, <a href="/A001296/a001296.pdf">The operator (xD)^n</a>, J. Indian Math. Soc., 15 (1923),3-4. [Annotated scanned copy]

%F From _Alois P. Heinz_, Jul 04 2015: (Start)

%F G.f.: (24*x^3+58*x^2+22*x+1)*x/(x-1)^8.

%F a(n) = n^3*(n+3)*(n+2)*(n+1)^2/48.

%F a(n) = n*Stirling2(n+3,n). (End)

%p a:= n-> n^3*(n+3)*(n+2)*(n+1)^2/48:

%p seq(a(n), n=1..40);  # _Alois P. Heinz_, Jul 04 2015

%Y This is the seventh sequence in the sequence A000027, A000217, A002411, A001296, A108650, A001297, ...

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Jun 30 2015

%E More terms from _Alois P. Heinz_, Jul 04 2015