A381285
Expansion of e.g.f. 1/(1 - sin(2*x) / 2).
Original entry on oeis.org
1, 1, 2, 2, -8, -104, -688, -3088, -128, 209536, 3145472, 29795072, 139389952, -1715047424, -60056147968, -1004215072768, -10305404960768, -1945682345984, 2949643589844992, 84438462955323392, 1458284922371571712, 12032890515685113856, -245515800089314459648
Offset: 0
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With[{nn=30},CoefficientList[Series[1/(1-Sin[2x]/2),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jul 09 2025 *)
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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, k!*(2*I)^(n-k)*a136630(n, k));
A381278
Expansion of e.g.f. exp(sin(3*x) / 3).
Original entry on oeis.org
1, 1, 1, -8, -35, -8, 1117, 6328, -19943, -513728, -2096711, 30574720, 447401845, 23791744, -59033858219, -527680180736, 4971322421425, 144677554315264, 430091284739185, -27641200139694080, -398305237630617971, 2876369985206861824, 145441158283475935309
Offset: 0
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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, (3*I)^(n-k)*a136630(n, k));
A381346
Expansion of e.g.f. 1/( 1 - sinh(sqrt(2)*x) / sqrt(2) ).
Original entry on oeis.org
1, 1, 2, 8, 40, 244, 1808, 15632, 154240, 1712656, 21132032, 286800128, 4246266880, 68108302144, 1176458774528, 21772909267712, 429818456473600, 9015349812633856, 200218257664704512, 4693597812326094848, 115820240623410872320, 3000905720793597113344
Offset: 0
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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, k!*2^((n-k)/2)*a136630(n, k));
A381347
Expansion of e.g.f. 1/( 1 - sin(sqrt(2)*x) / sqrt(2) ).
Original entry on oeis.org
1, 1, 2, 4, 8, 4, -112, -1184, -9088, -59504, -310528, -643136, 14701568, 323581504, 4554426368, 51666451456, 458243735552, 2004840714496, -37024075153408, -1386061762251776, -29290212127670272, -483475390212586496, -6224109737622372352, -45231727252157947904
Offset: 0
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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, k!*(-2)^((n-k)/2)*a136630(n, k));
Showing 1-4 of 4 results.