A186763 -id:A186763 - cp's OEIS frontend

A349088 a(n) = n! * Sum_{k=0..floor((n-1)/3)} 1 / (3*k+1)!.

0, 1, 2, 6, 25, 125, 750, 5251, 42008, 378072, 3780721, 41587931, 499055172, 6487717237, 90828041318, 1362420619770, 21798729916321, 370578408577457, 6670411354394226, 126737815733490295, 2534756314669805900, 53229882608065923900, 1171057417377450325801

Offset: 0

Ilya Gutkovskiy, Mar 25 2022

nonn

Cf. A002627, A009628, A143820, A186763, A337725, A349089, A352659.

Table[n! Sum[1/(3 k + 1)!, {k, 0, Floor[(n - 1)/3]}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[(Exp[x] - 2 Exp[-x/2] Sin[(Pi - 3 Sqrt[3] x)/6])/(3 (1 - x)), {x, 0, nmax}], x] Range[0, nmax]!

E.g.f.: (exp(x) - 2 * exp(-x/2) * sin((Pi - 3*sqrt(3)*x)/6)) / (3*(1 - x)).

a(n) = floor(c * n!) for n > 0, where c = 1.041865355... = A143820.

A349089 a(n) = n! * Sum_{k=0..floor((n-1)/4)} 1 / (4*k+1)!.

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Mar 25 2022

nonn

Cf. A002627, A009628, A186763, A334363, A337728, A349088, A352660.

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]!

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

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

cp's OEIS Frontend

A349088 a(n) = n! * Sum_{k=0..floor((n-1)/3)} 1 / (3*k+1)!.

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