A121945 a(n) is the sum of the first n factorials in decreasing powers from n to 1. a(n) = Sum_{k = 1..n} k!^(n-k+1).

1, 3, 11, 69, 929, 30273, 2591057, 614059329, 423463272449, 907403624202753, 6082394749206781697, 140440480114401911810049, 10845109029138237198786147329, 3088811811740393517911301490890753, 3220352134317904958924570965080200574977, 12657255883388612328426763834234183884771442689

Offset: 1

Author

Tanya Khovanova, Sep 03 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..58

Crossrefs

Similar to A003101 = Sum_{k = 1..n} (n-k+1)^k - only with inserted factorials.

Programs

GAP

List([1..20], n-> Sum([1..n], j-> Factorial(j)^(n-j+1)) ); # G. C. Greubel, Oct 07 2019

Magma

[(&+[Factorial(j)^(n-j+1): j in [1..n]]): n in [1..20]]; // G. C. Greubel, Oct 07 2019

Maple

seq(add(factorial(j)^(n-j+1), j=1..n), n=1..20); # G. C. Greubel, Oct 07 2019

Mathematica

Table[Sum[Factorial[i]^(n-i+1), {i, n}], {n, 20}]

PARI

vector(20, n, sum(j=1, n, (j!)^(n-j+1)) ) \\ G. C. Greubel, Oct 07 2019

Sage

[sum(factorial(j)^(n-j+1) for j in (1..n)) for n in (1..20)] # G. C. Greubel, Oct 07 2019

Extensions

More terms from G. C. Greubel, Oct 07 2019