A381310
E.g.f. A(x) satisfies A(x) = exp( sin(x * A(x)^(1/2)) / A(x)^(1/2) ).
Original entry on oeis.org
1, 1, 1, 0, -7, -38, -111, 259, 7025, 59752, 209297, -2545257, -59541487, -609139048, -1257456543, 86370090271, 1968628674465, 20998208227456, -60103780767519, -7806917233342465, -175430347192682527, -1683391495632464904, 26661441929560502097, 1550891419460475900175
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/2-k/2+1)^(k-1)*I^(n-k)*a136630(n, k));
A381343
Expansion of e.g.f. exp( sin(sqrt(2)*x) / sqrt(2) ).
Original entry on oeis.org
1, 1, 1, -1, -7, -15, 25, 287, 721, -2847, -30255, -61697, 682761, 5861713, 3105193, -258188513, -1681060063, 4623681473, 135471132705, 564325398271, -6357495670375, -89817656595791, -84337394884167, 7820620314702879, 67277670159083761, -322108989883888479
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-k)/2)*a136630(n, k));
A381383
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)) / A(x) )^2.
Original entry on oeis.org
1, 2, 6, 26, 176, 1842, 25552, 417146, 7727232, 162203810, 3855123968, 102712106202, 3024863555584, 97316416451282, 3393616911181824, 127581806046438074, 5147059194652983296, 221843071154521998402, 10172731970828970557440, 494451746675777509028762
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) = 2*sum(k=0, n, k!*binomial(2*n-k+2, k)/(2*n-k+2)*a136630(n, k));
A381385
E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)) / A(x) )^2.
Original entry on oeis.org
1, 2, 6, 22, 64, -398, -14768, -288458, -4695168, -62117470, -385004032, 15463485398, 923640068096, 33487329741842, 957927747201024, 20185023268062070, 95909717192212480, -21197461265149558718, -1619210077600334151680, -82170388240550451506282, -3226620083793471277105152
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) = 2*sum(k=0, n, k!*binomial(2*n-k+2, k)/(2*n-k+2)*I^(n-k)*a136630(n, k));
A381412
E.g.f. A(x) satisfies A(x) = exp( 2 * sinh(x * A(x)) / A(x) ).
Original entry on oeis.org
1, 2, 4, 10, 64, 754, 9024, 109050, 1544960, 27480162, 567449600, 12641553258, 303021248512, 7982668175954, 231306526932992, 7245659221444186, 242226980924424192, 8623216994933650114, 327015684198600278016, 13169904418920596839626, 560434137147666884198400
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) = 2*sum(k=0, n, (2*n-2*k+2)^(k-1)*a136630(n, k));
A381414
E.g.f. A(x) satisfies A(x) = exp( 2 * sin(x * A(x)) / A(x) ).
Original entry on oeis.org
1, 2, 4, 6, -32, -686, -8256, -72394, -200448, 11160866, 373370880, 7696016614, 100295200768, -338643776142, -77999443329024, -3211092423560938, -85537972638318592, -1169784729390416830, 33029632126142382080, 3381750252027454249926, 158090250687453045194752
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) = 2*sum(k=0, n, (2*n-2*k+2)^(k-1)*I^(n-k)*a136630(n, k));
A381416
E.g.f. A(x) satisfies A(x) = exp( 2 * sinh(x * A(x)) ).
Original entry on oeis.org
1, 2, 12, 130, 2080, 44354, 1185856, 38188546, 1439993088, 62261776002, 3037542875136, 165090563653250, 9892965209886720, 648064548551770562, 46075919968420085760, 3533725068594022938626, 290804441398399410503680, 25561250854199444302177538, 2390133356713125694150017024
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) = 2*sum(k=0, n, (2*n+2)^(k-1)*a136630(n, k));
A381418
E.g.f. A(x) satisfies A(x) = exp( 2 * sin(x * A(x)) ).
Original entry on oeis.org
1, 2, 12, 126, 1920, 38594, 966336, 29013502, 1016725248, 40756464002, 1840019388416, 92407718510206, 5110719354064896, 308687318601431618, 20219267260662005760, 1427631259848921544702, 108098847179804608299008, 8738141126983786551626498, 751078053821468153074155520
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) = 2*sum(k=0, n, (2*n+2)^(k-1)*I^(n-k)*a136630(n, k));