A357662
Expansion of e.g.f. cosh( (exp(3*x) - 1)/sqrt(3) ).
Original entry on oeis.org
1, 0, 3, 27, 198, 1485, 12825, 132678, 1582497, 20603727, 284290560, 4132840239, 63571690485, 1038868740000, 18022911716439, 330305863479615, 6355242571945878, 127721845479277737, 2672729031195365949, 58142565625982730462, 1313557910179640120061
Offset: 0
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my(N=30, x='x+O('x^N)); apply(round, Vec(serlaplace(cosh((exp(3*x)-1)/sqrt(3)))))
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a(n) = sum(k=0, n\2, 3^(n-k)*stirling(n, 2*k, 2));
A357664
Expansion of e.g.f. sinh( (exp(2*x) - 1)/sqrt(2) )/sqrt(2).
Original entry on oeis.org
0, 1, 2, 6, 32, 220, 1592, 11944, 96000, 847120, 8209952, 86020704, 958326272, 11243157952, 138464594816, 1789358629504, 24250275913728, 344002396594432, 5092763802452480, 78443316497892864, 1253887341918199808, 20761127890765634560
Offset: 0
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my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sinh((exp(2*x)-1)/sqrt(2))/sqrt(2)))))
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a(n) = sum(k=0, (n-1)\2, 2^(n-1-k)*stirling(n, 2*k+1, 2));
A357666
Expansion of e.g.f. sinh( (exp(4*x) - 1)/2 )/2.
Original entry on oeis.org
0, 1, 4, 20, 160, 1872, 25024, 348224, 5055488, 78571776, 1332573184, 24695206912, 493816963072, 10492449771520, 234399640633344, 5480635606908928, 134015043318054912, 3427700843478056960, 91642829715498336256, 2556218693498006929408
Offset: 0
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh((exp(4*x)-1)/2)/2)))
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a(n) = sum(k=0, (n-1)\2, 4^(n-1-k)*stirling(n, 2*k+1, 2));
Showing 1-3 of 3 results.