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));
A381384
E.g.f. A(x) satisfies A(x) = 1/( 1 - sin(x * A(x)^2) / A(x)^2 ).
Original entry on oeis.org
1, 1, 2, 5, 0, -299, -5840, -90791, -1210496, -11174519, 71397888, 8367496301, 327020705792, 9709296136541, 226223975684096, 2946493117173761, -87437164233621504, -9675847870039338095, -535455805780063748096, -22518479178045130002731, -706013052362778282033152
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)*I^(n-k)*a136630(n, k));
A381377
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * cosh(x * A(x)) )^2.
Original entry on oeis.org
1, 2, 6, 30, 288, 4090, 68160, 1292774, 28627200, 739821618, 21729070080, 708442911022, 25365382259712, 992297344710698, 42173572623716352, 1934344590577340790, 95175474351245230080, 5000227637170108004194, 279428527333796676894720, 16552583621200571079876158
Offset: 0
-
a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = 2*sum(k=0, n, k!*binomial(2*n-k+2, k)/(2*n-k+2)*a185951(n, k));
A381407
E.g.f. A(x) satisfies A(x) = exp( x * cosh(x * A(x)^2) ).
Original entry on oeis.org
1, 1, 1, 4, 61, 756, 8581, 125168, 2577849, 60269968, 1469636041, 39496750272, 1212192326005, 41147125079360, 1496063100479949, 58263746530145536, 2447130544401729649, 110270888250759852288, 5279535712822539622033, 267412182631190346232832
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, (2*n-2*k+1)^(k-1)*a185951(n, k));
Showing 1-5 of 5 results.
Comments