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A330021
Expansion of e.g.f. exp(sinh(exp(x) - 1)).
2
1, 1, 2, 6, 25, 128, 754, 5001, 37048, 303930, 2732395, 26657106, 280039786, 3149224991, 37729906686, 479570263690, 6442902231289, 91186621152460, 1355582225366134, 21112253012491481, 343672026658191836, 5834977672879651390, 103130592695715620419
OFFSET
0,3
COMMENTS
Stirling transform of A003724.
Exponential transform of A024429.
LINKS
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k) * A003724(k).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A024429(k) * a(n-k).
MAPLE
g:= proc(n) option remember; `if`(n=0, 1, add(
binomial(n-1, j-1)*irem(j, 2)*g(n-j), j=1..n))
end:
b:= proc(n, m) option remember; `if`(n=0,
g(m), m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..22); # Alois P. Heinz, Jun 23 2023
MATHEMATICA
nmax = 22; CoefficientList[Series[Exp[Sinh[Exp[x] - 1]], {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Nov 27 2019
STATUS
approved