

A330021


Expansion of e.g.f. exp(sinh(exp(x)  1)).


1



1, 1, 2, 6, 25, 128, 754, 5001, 37048, 303930, 2732395, 26657106, 280039786, 3149224991, 37729906686, 479570263690, 6442902231289, 91186621152460, 1355582225366134, 21112253012491481, 343672026658191836, 5834977672879651390, 103130592695715620419
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OFFSET

0,3


COMMENTS

Stirling transform of A003724.
Exponential transform of A024429.


LINKS

Table of n, a(n) for n=0..22.


FORMULA

a(n) = Sum_{k=0..n} Stirling2(n,k) * A003724(k).
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n1,k1) * A024429(k) * a(nk).


MATHEMATICA

nmax = 22; CoefficientList[Series[Exp[Sinh[Exp[x]  1]], {x, 0, nmax}], x] Range[0, nmax]!


CROSSREFS

Cf. A003724, A009218, A011800, A024429, A080831.
Sequence in context: A030907 A325576 A130619 * A181594 A030915 A030921
Adjacent sequences: A330018 A330019 A330020 * A330022 A330023 A330024


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Nov 27 2019


STATUS

approved



