A009200
E.g.f. exp(sin(log(1+x))).
Original entry on oeis.org
1, 1, 0, -1, 2, -4, 16, -120, 1084, -10568, 111196, -1269764, 15728360, -210510936, 3029497472, -46654106824, 765497451536, -13330741903360, 245546485746064, -4769321293582128, 97417091239222336, -2087367002843576384, 46814167766826521920, -1096698328458955351616
Offset: 0
A009206
Expansion of e.g.f.: exp(sin(x))*x.
Original entry on oeis.org
0, 1, 2, 3, 0, -15, -48, -21, 448, 1953, 640, -32461, -152064, 77649, 4331264, 18557595, -46686208, -894805183, -2948087808, 21405607651, 254321049600, 421226202033, -10904188190720, -90171090228021, 96102216892416, 6418365899545825
Offset: 0
-
With[{nn=30},CoefficientList[Series[Exp[Sin[x]]*x,{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Dec 25 2021 *)
Definition clarified and prior Mathematica program replaced by
Harvey P. Dale, Dec 25 2021
A293021
a(n) = n! * [x^n] exp(n*sin(x)).
Original entry on oeis.org
1, 1, 4, 24, 192, 1880, 21312, 266504, 3469312, 42094656, 297625600, -8727514752, -659406274560, -31019532622208, -1314656227540992, -54314985911216640, -2248955319931633664, -94369141109824233472, -4028982346754921594880, -175032005028072692797440
Offset: 0
-
Table[n! SeriesCoefficient[Exp[n Sin[x]], {x, 0, n}], {n, 0, 19}]
A381343
Expansion of e.g.f. exp( sin(sqrt(2)*x) / sqrt(2) ).
Original entry on oeis.org
1, 1, 1, -1, -7, -15, 25, 287, 721, -2847, -30255, -61697, 682761, 5861713, 3105193, -258188513, -1681060063, 4623681473, 135471132705, 564325398271, -6357495670375, -89817656595791, -84337394884167, 7820620314702879, 67277670159083761, -322108989883888479
Offset: 0
-
a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (-2)^((n-k)/2)*a136630(n, k));