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));
A385305
Expansion of e.g.f. 1/(1 - 3 * sinh(x))^(1/3).
Original entry on oeis.org
1, 1, 4, 29, 296, 3921, 63904, 1236509, 27700096, 705098241, 20100847104, 634406699389, 21959759364096, 827184049670161, 33684401687855104, 1474548883501060669, 69051807696652599296, 3444499079760040247681, 182339939994632235515904, 10209271857672376613472349
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)*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));
A385309
Expansion of e.g.f. 1/(1 - 3 * x * cosh(x))^(1/3).
Original entry on oeis.org
1, 1, 4, 31, 328, 4485, 75520, 1509347, 34916224, 917703145, 27011107840, 880133628231, 31451749424128, 1223047891889837, 51414400611438592, 2323391075748100555, 112315439676217262080, 5783449255108473820497, 316034972288791445241856, 18265740423344520141491951
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k)*a185951(n, k));
A385372
Expansion of e.g.f. 1/(1 - 3 * arcsinh(x))^(1/3).
Original entry on oeis.org
1, 1, 4, 27, 264, 3369, 52896, 986187, 21293184, 522491697, 14359993344, 436964488443, 14583637923840, 529683272760537, 20798444046458880, 877927319167721067, 39644175780617748480, 1906959640776766940385, 97344936393086594580480, 5255894631271228490720475
Offset: 0
Showing 1-5 of 5 results.