A193563 a(0) = 0, a(n) = n^2 * (a(n-1) + 1).

0, 1, 8, 81, 1312, 32825, 1181736, 57905113, 3705927296, 300180111057, 30018011105800, 3632179343801921, 523033825507476768, 88392716510763573961, 17324972436109660496552, 3898118798124673611724425, 997918412319916444601453056

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..250

Formula

From Seiichi Manyama, Jan 05 2024: (Start)

a(n) = (n!)^2 * Sum_{k=0..n} (k/k!)^2.

a(n) = n^2 * A006040(n-1) for n > 0. (End)

a(n) = Sum_{k=1..n} (k!*binomial(n,k))^2. - Ridouane Oudra, Jun 14 2025

a(n) = n^2 + BesselI(0,2)*(n!)^2 - n^2*hypergeom([1], [n, n], 1) for n > 0. - Stefano Spezia, Jun 14 2025

Maple

seq(n!^2*add(1/k!^2, k=0..n-1), n=0..16);   # Mark van Hoeij, May 13 2013

Mathematica

FoldList[#2^2*(# + 1) &, Range[0, 20]] (* Paolo Xausa, Jun 18 2025 *)

Prog

(PARI) a=[0]; for(n=1, 20, a=concat(a, (a[#a]+1)*n^2)); a \\ Charles R Greathouse IV, Jul 31 2011

Crossrefs

Cf. A006040, A007526 (multiply by n instead of n^2), A180255.

Sequence in context: A092366 A022519 A138439 * A026845 A305770 A145921

Adjacent sequences: A193560 A193561 A193562 * A193564 A193565 A193566

Keyword

nonn,easy

Author

Meherzad Lahewala, Jul 31 2011

Status

approved