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A036781 a(n) = n + Sum_{k=0..n} k!. 2

%I #16 Jan 31 2023 13:29:33

%S 1,3,6,13,38,159,880,5921,46242,409123,4037924,43954725,522956326,

%T 6749977127,93928268328,1401602636329,22324392524330,378011820620331,

%U 6780385526348332,128425485935180333,2561327494111820334,53652269665821260335,1177652997443428940336

%N a(n) = n + Sum_{k=0..n} k!.

%H Alois P. Heinz, <a href="/A036781/b036781.txt">Table of n, a(n) for n = 0..400</a>

%p a:= proc(n) option remember; `if`(n=0, 1, a(n-1)+1+n!) end:

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Jan 05 2015

%t Module[{nn=30,f},f=Accumulate[Range[0,nn]!];Table[n+f[[n]],{n,nn}]]-1 (* _Harvey P. Dale_, Nov 04 2020 *)

%t Module[{nn=30,f},f=Accumulate[Range[0,nn]!];Total/@Thread[{f,Range[0,nn]}]] (* _Harvey P. Dale_, Jan 31 2023 *)

%Y A003422[ n ] + n.

%Y Cf. A007489.

%K nonn

%O 0,2

%A _N. J. A. Sloane_.

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)