A357661
Expansion of e.g.f. cosh( (exp(2*x) - 1)/sqrt(2) ).
Original entry on oeis.org
1, 0, 2, 12, 60, 320, 2040, 15568, 133648, 1230336, 11962400, 123144384, 1349008320, 15731096576, 194349866880, 2527082917120, 34392647418112, 488243791183872, 7216792525799936, 110936087161801728, 1771199461131500544, 29324602146652307456
Offset: 0
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With[{nn=30},CoefficientList[Series[Cosh[(Exp[2x]-1)/Sqrt[2]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 23 2025 *)
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my(N=30, x='x+O('x^N)); apply(round, Vec(serlaplace(cosh((exp(2*x)-1)/sqrt(2)))))
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a(n) = sum(k=0, n\2, 2^(n-k)*stirling(n, 2*k, 2));
A357663
Expansion of e.g.f. cosh( (exp(4*x) - 1)/2 ).
Original entry on oeis.org
1, 0, 4, 48, 464, 4480, 48448, 621824, 9320704, 154890240, 2746131456, 51237908480, 1007228375040, 20965557829632, 463091379159040, 10826828061147136, 266438312153120768, 6861616219559034880, 184128217520198123520, 5135753969867535941632
Offset: 0
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With[{nn=20},CoefficientList[Series[Cosh[(Exp[4x]-1)/2],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 13 2025 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(cosh((exp(4*x)-1)/2)))
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a(n) = sum(k=0, n\2, 4^(n-k)*stirling(n, 2*k, 2));
A357665
Expansion of e.g.f. sinh( (exp(3*x) - 1)/sqrt(3) )/sqrt(3).
Original entry on oeis.org
0, 1, 3, 12, 81, 765, 7938, 85239, 963819, 11801862, 158533443, 2320621569, 36425289816, 604576791405, 10532817901791, 192197187209484, 3673078679995677, 73486862051182425, 1536507360834633666, 33482575797899354235, 758209049155176114807
Offset: 0
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my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sinh((exp(3*x)-1)/sqrt(3))/sqrt(3)))))
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a(n) = sum(k=0, (n-1)\2, 3^(n-1-k)*stirling(n, 2*k+1, 2));
Showing 1-3 of 3 results.