OFFSET
0,2
FORMULA
a(n) = n! * Sum_{k=0..n} Stirling2(n+1,k+1) / k!.
MATHEMATICA
nmax = 18; CoefficientList[Series[Exp[x] BesselI[0, 2 Sqrt[Exp[x] - 1]], {x, 0, nmax}], x] Range[0, nmax]!^2
Table[n! Sum[StirlingS2[n + 1, k + 1]/k!, {k, 0, n}], {n, 0, 18}]
PROG
(PARI) a(n) = n! * sum(k=0, n, stirling(n+1, k+1, 2) / k!); \\ Michel Marcus, Jul 27 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 26 2020
STATUS
approved