A381147
E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)) / A(x) ).
Original entry on oeis.org
1, 1, 1, 2, 13, 92, 621, 5112, 56057, 705168, 9480665, 141039648, 2366242693, 43609330624, 864164283269, 18414385180544, 422574196387953, 10374625080684800, 270563138370828465, 7472794772378583552, 218190569313134267517, 6714970997524417977344
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, (n-k+1)^(k-1)*a136630(n, k));
A381177
E.g.f. A(x) satisfies A(x) = 1/( 1 - A(x) * sinh(x * A(x)) ).
Original entry on oeis.org
1, 1, 6, 73, 1352, 33861, 1072000, 41083477, 1849680768, 95708731945, 5597075177984, 365091888890433, 26281788308598784, 2069729710424907181, 177006820644852031488, 16337090667286093559821, 1618592591411194127089664, 171337824188415839421148881, 19299478529228162963028508672
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, k!*binomial(n+2*k+1, k)/(n+2*k+1)*a136630(n, k));
A381179
E.g.f. A(x) satisfies A(x) = 1 + sinh(x*A(x)) / A(x).
Original entry on oeis.org
1, 1, 0, 1, 8, 21, 64, 1093, 8448, 47785, 654848, 9402537, 94222336, 1264390141, 23392960512, 363389219053, 5722054885376, 117602664867921, 2434091053613056, 47867013812467921, 1080303165427679232, 26716998341391367141, 645003218568158904320, 16403742152044108508181
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, k!*binomial(n-k+1, k)/(n-k+1)*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
-
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
-
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));
A381411
E.g.f. A(x) satisfies A(x) = exp( sinh(x * A(x)^2) / A(x)^2 ).
Original entry on oeis.org
1, 1, 1, 2, 21, 252, 2645, 29248, 420777, 7789008, 160214281, 3480537568, 82299294077, 2172147323712, 63112534885725, 1969853583132672, 65473850077772881, 2323179959573426432, 88007266294215935121, 3540245668453458467328, 150353926528453088942821
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-2*k+1)^(k-1)*a136630(n, k));
A381413
E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^2) / A(x)^2 ).
Original entry on oeis.org
1, 1, 1, 0, -19, -248, -2355, -14504, 69113, 4886848, 117560921, 1925294976, 14523966437, -478472693632, -28832809713435, -921278399444480, -18983574162924687, -55161522627854336, 18306724696454977713, 1118400460045234098176, 41755736397548337559133
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-2*k+1)^(k-1)*I^(n-k)*a136630(n, k));
A381417
E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^2) ).
Original entry on oeis.org
1, 1, 5, 48, 693, 13432, 327561, 9639224, 332476361, 13157303104, 587704852749, 29250533304960, 1605304225302525, 96313936238637184, 6271774683977444817, 440545491471769836032, 33204015428071302059025, 2672942015998405569765376, 228892490007003118401996565
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+1)^(k-1)*I^(n-k)*a136630(n, k));
A381428
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x) * A(x)^2 ).
Original entry on oeis.org
1, 1, 6, 73, 1344, 33481, 1054656, 40223233, 1802385024, 92827015921, 5403527705856, 350854589607193, 25142008355656704, 1971003462240791161, 167802783944207917056, 15417877986778302551953, 1520661128893781018640384, 160249491538400609431567201, 17969682580669053325124960256
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, k!*binomial(3*k+1,k)/(3*k+1)*a136630(n, k));
A381429
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x) * A(x)^3 ).
Original entry on oeis.org
1, 1, 8, 133, 3392, 117601, 5167808, 275334613, 17250670592, 1242994578721, 101273185092608, 9206681997173893, 923928346115182592, 101453787213382443841, 12100018549609932996608, 1557645163271323384461973, 215265839194368088629051392, 31788685348087376561935104961
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, k!*binomial(4*k+1, k)/(4*k+1)*a136630(n, k));