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A371831
a(n) = numerator(Sum_{k=1..n} k^2/k!).
1
0, 1, 3, 9, 31, 43, 217, 3913, 9133, 73067, 1972819, 6576067, 24112247, 372017527, 1612075951, 157983443203, 7109254944151, 37916026368811, 644572448269793, 34806912206568841, 2422459091299663, 7775794614048301, 277759159408419360043, 2036900502328408640323, 46848711553553398727437
OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Incomplete Gamma Function.
FORMULA
a(n) = numerator((2*(e*Gamma(n+1, 1) - 1) - n)/n!).
a(n) = numerator(A030297(n)/n!).
Limit_{n->oo} a(n)/A371832(n) = 2*e = A019762.
MATHEMATICA
a[n_]:=Numerator[(2(E*Gamma[n+1, 1]-1)-n)/n!]; Array[a, 25, 0]
PROG
(PARI) a(n) = numerator(sum(k=1, n, k^2/k!)); \\ Michel Marcus, Apr 07 2024
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Stefano Spezia, Apr 07 2024
STATUS
approved