A381378
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cos(x * A(x)^2) ).
Original entry on oeis.org
1, 1, 2, 3, -48, -1135, -18240, -231637, -1356544, 53849889, 3026119680, 100808786419, 2429052865536, 26284690243825, -1539261873164288, -140633348417624805, -7196339681250508800, -258335768147494234303, -4225401456668904259584, 307227604973975435785571
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, k!*binomial(2*n-k+1, k)/(2*n-k+1)*I^(n-k)*a185951(n, k));
A381382
E.g.f. A(x) satisfies A(x) = 1/( 1 - sinh(x * A(x)^2) / A(x)^2 ).
Original entry on oeis.org
1, 1, 2, 7, 48, 541, 7600, 120891, 2178176, 45053401, 1065957888, 28344376303, 831973593088, 26647344263541, 925300511922176, 34668496386129763, 1394928344160731136, 59986286728056665905, 2744940504174063714304, 133158543838350039763671
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(2*n-k+1, k)/(2*n-k+1)*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));
Showing 1-3 of 3 results.
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