A385310
Expansion of e.g.f. 1/(1 - 2 * x * cos(x))^(1/2).
Original entry on oeis.org
1, 1, 3, 12, 69, 500, 4455, 46928, 571977, 7914384, 122585355, 2100940864, 39470867469, 806555184448, 17808628411119, 422498774818560, 10717948285126545, 289501146405400832, 8295124400250875667, 251300745071590317056, 8025654235707259740885, 269482309052945201181696
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)*I^(n-k)*a185951(n, k));
A385304
Expansion of e.g.f. 1/(1 - 2 * sinh(x))^(1/2).
Original entry on oeis.org
1, 1, 3, 16, 117, 1096, 12543, 169576, 2644617, 46735936, 922993083, 20145579136, 481555537917, 12511452674176, 351058439096823, 10579734482269696, 340820224678288017, 11687491783287586816, 425075150516293691763, 16343274366458168160256, 662325275389743380902917
Offset: 0
-
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)*a136630(n, k));
A385307
Expansion of e.g.f. 1/(1 - 3 * sin(x))^(1/3).
Original entry on oeis.org
1, 1, 4, 27, 264, 3361, 52704, 981707, 21176704, 519150241, 14255163904, 433384277787, 14451212550144, 524406240059521, 20572970822959104, 867641565719168267, 39145118179183427584, 1881294510800399083201, 95950279080398196834304, 5176039012712211526485147
Offset: 0
-
a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k)*I^(n-k)*a136630(n, k));
A385308
Expansion of e.g.f. 1/(1 - 2 * x * cosh(x))^(1/2).
Original entry on oeis.org
1, 1, 3, 18, 141, 1400, 17055, 245392, 4070073, 76483584, 1606033755, 37267953536, 947051118981, 26156846230528, 780174007426359, 24992424003517440, 855795857724702705, 31193844533488074752, 1205893835653392258867, 49280187764171870470144, 2122704756621224015194365
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)*a185951(n, k));
Showing 1-4 of 4 results.