A235134
Expansion of e.g.f. 1/(1 - sinh(2*x))^(1/2).
Original entry on oeis.org
1, 1, 3, 19, 153, 1561, 19563, 289339, 4932273, 95258161, 2055639123, 49019157859, 1280056939593, 36329281202761, 1113449691889083, 36651273215389579, 1289577677407798113, 48299079453732363361, 1918528841276621473443, 80559757274836073592499
Offset: 0
-
CoefficientList[Series[1/(1-Sinh[2*x])^(1/2), {x, 0, 20}], x] * Range[0, 20]!
-
x='x+O('x^50); Vec(serlaplace(1/(sqrt(1-sinh(2*x))))) \\ G. C. Greubel, Apr 05 2017
-
a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k)*2^(n-k)*a136630(n, k)); \\ Seiichi Manyama, Jun 24 2025
A385281
Expansion of e.g.f. 1/(1 - 2 * x * cosh(2*x))^(1/2).
Original entry on oeis.org
1, 1, 3, 27, 249, 2825, 41355, 708883, 13888497, 309267729, 7698772755, 211585744139, 6367841422569, 208299923870233, 7357493992966299, 279095125351544835, 11316313498670411745, 488403056864943302177, 22355228989851909617187, 1081663315375339026249211
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k)*2^(n-k)*a185951(n, k));
A385283
Expansion of e.g.f. 1/(1 - 2 * x * cos(2*x))^(1/2).
Original entry on oeis.org
1, 1, 3, 3, -39, -775, -9045, -85813, -426447, 7321329, 325555155, 7786757011, 137053423881, 1388713844713, -21121997539461, -1827406866674085, -69034283067822495, -1852635543265039903, -30574875232261547613, 308376017794648053539, 54871741689019890859065
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k)*(2*I)^(n-k)*a185951(n, k));
A380156
Expansion of e.g.f. 1/(1 - 3*x*exp(3*x))^(1/3).
Original entry on oeis.org
1, 1, 10, 127, 2260, 52165, 1478098, 49666267, 1930817080, 85253566825, 4214519350750, 230609701370719, 13837049296702228, 903380930924784013, 63754235596937808874, 4836352735401636409795, 392451456493513697671792, 33920902255644870783973201, 3111255003645991777552833718
Offset: 0
Showing 1-4 of 4 results.
Comments