A349089 - OEIS

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A349089

a(n) = n! * Sum_{k=0..floor((n-1)/4)} 1 / (4*k+1)!.

0, 1, 2, 6, 24, 121, 726, 5082, 40656, 365905, 3659050, 40249550, 482994600, 6278929801, 87905017214, 1318575258210, 21097204131360, 358652470233121, 6455744464196178, 122659144819727382, 2453182896394547640, 51516840824285500441, 1133370498134281009702

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OFFSET

0,3

LINKS

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

FORMULA

E.g.f.: (sin(x) + sinh(x)) / (2*(1 - x)).

a(n) = floor(c * n!) for n > 0, where c = 1.008336089... = A334363.

MATHEMATICA

Table[n! Sum[1/(4 k + 1)!, {k, 0, Floor[(n - 1)/4]}], {n, 0, 22}]

nmax = 22; CoefficientList[Series[(Sin[x] + Sinh[x])/(2 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS