A332256
E.g.f.: 1 / (2 - exp(sinh(x))).
Original entry on oeis.org
1, 1, 3, 14, 87, 672, 6231, 67412, 833475, 11593140, 179170947, 3045978388, 56490392943, 1134970258372, 24557211519951, 569294311105300, 14077429483372251, 369861235318338404, 10289111057247180411, 302132879478864660340, 9338874072977661538119
Offset: 0
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nmax = 20; CoefficientList[Series[1/(2 - Exp[Sinh[x]]), {x, 0, nmax}], x] Range[0, nmax]!
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seq(n)={Vec(serlaplace(1/(2 - exp(sinh(x + O(x*x^n))))))} \\ Andrew Howroyd, Feb 08 2020
A346749
E.g.f.: exp( (x * (1 + x) * exp(x) - sinh(x)) / 4 ).
Original entry on oeis.org
1, 0, 1, 2, 7, 26, 124, 628, 3565, 22096, 149176, 1080868, 8372543, 68957268, 601351748, 5528967282, 53416626441, 540682811424, 5718911631856, 63060992662328, 723382253378395, 8616075340134868, 106374847828850676, 1359171823319541070, 17946987240664242493
Offset: 0
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nmax = 24; CoefficientList[Series[Exp[(x (1 + x) Exp[x] - Sinh[x])/4], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Floor[k^2/4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
A372508
Expansion of e.g.f. exp(sinh(x)) - exp(cosh(x) - 1).
Original entry on oeis.org
0, 1, 0, 2, 1, 12, 6, 128, 78, 1872, 1613, 37600, 38336, 990784, 1124280, 32333824, 41622181, 1272660224, 1843050734, 59527313920, 94591980910, 3252626013184, 5602035320753, 204354574172160, 380190518533920, 14594815769038848, 29179899891380592, 1174376539738169344
Offset: 0
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nmax = 27; CoefficientList[Series[Exp[Sinh[x]] - Exp[Cosh[x] - 1], {x, 0, nmax}], x] Range[0, nmax]!
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