A357649
Expansion of e.g.f. cosh( (exp(3*x) - 1)/3 ).
Original entry on oeis.org
1, 0, 1, 9, 64, 435, 3097, 24822, 232759, 2517345, 30070954, 382827225, 5110770205, 71421582024, 1049487311485, 16286699945853, 267145966335088, 4616924929100535, 83622792656855125, 1578916985654901366, 30957723637379211115, 628927539690331202661
Offset: 0
-
With[{m = 20}, Range[0, m]! * CoefficientList[Series[Cosh[(Exp[3*x] - 1)/3], {x, 0, m}], x]] (* Amiram Eldar, Oct 07 2022 *)
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(cosh((exp(3*x)-1)/3)))
-
a(n) = sum(k=0, n\2, 3^(n-2*k)*stirling(n, 2*k, 2));
A357617
Expansion of e.g.f. sinh( (exp(4*x) - 1)/4 ).
Original entry on oeis.org
0, 1, 4, 17, 88, 657, 6844, 83393, 1072880, 14242785, 197046964, 2895895345, 45930435016, 789930042865, 14628150636012, 287915593953889, 5950831121362656, 128180962018224833, 2868724306984850020, 66704877850797014353, 1613138176448134032440
Offset: 0
-
With[{m = 20}, Range[0, m]! * CoefficientList[Series[Sinh[(Exp[4*x] - 1)/4], {x, 0, m}], x]] (* Amiram Eldar, Oct 07 2022 *)
-
my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh((exp(4*x)-1)/4))))
-
a(n) = sum(k=0, (n-1)\2, 4^(n-1-2*k)*stirling(n, 2*k+1, 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
-
my(N=30, x='x+O('x^N)); concat(0, apply(round, Vec(serlaplace(sinh((exp(3*x)-1)/sqrt(3))/sqrt(3)))))
-
a(n) = sum(k=0, (n-1)\2, 3^(n-1-k)*stirling(n, 2*k+1, 2));
A357668
Expansion of e.g.f. sinh( 3 * (exp(x) - 1) )/3.
Original entry on oeis.org
0, 1, 1, 10, 55, 307, 2026, 14779, 114157, 933616, 8110261, 74525167, 719925328, 7279859485, 76855303981, 845280487018, 9663800287483, 114601481983855, 1407040763488354, 17856103120048783, 233883061849700137, 3157648445216335528, 43887908697233605489
Offset: 0
-
my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(sinh(3*(exp(x)-1))/3)))
-
a(n) = sum(k=0, (n-1)\2, 9^k*stirling(n, 2*k+1, 2));
-
Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
a(n) = round((Bell_poly(n, 3)-Bell_poly(n, -3)))/6;
Showing 1-4 of 4 results.