A381171
Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + x*cosh(x)) ).
Original entry on oeis.org
1, 1, 2, 9, 72, 725, 8640, 124117, 2117248, 41477193, 913305600, 22371549761, 604476094464, 17858943664861, 572524035586048, 19793963392789965, 734249332747960320, 29090332675789113617, 1225991945551031304192, 54765451909152748484857, 2584803582762012599910400
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(n+1, k)*a185951(n, k))/(n+1);
A381173
Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + x*cos(x)) ).
Original entry on oeis.org
1, 1, 2, 3, -24, -475, -5760, -52297, -155008, 8781705, 313344000, 6966991339, 102864807936, 18664712365, -71473582229504, -3387816787568865, -103478592573112320, -1899945146589964783, 18941335827815596032, 3808766537454425974739, 215681241589289359769600
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(n+1, k)*I^(n-k)*a185951(n, k))/(n+1);
A381180
E.g.f. A(x) satisfies A(x) = 1 + sin(x*A(x)) / A(x).
Original entry on oeis.org
1, 1, 0, -1, -8, -19, 64, 1091, 7680, -1415, -650752, -8575865, -35559424, 857890021, 21380186112, 203548592651, -1615715926016, -95486152906639, -1599622990659584, -1397194164399601, 657963431581974528, 18168041375501245021, 157453907927886725120, -6059840564222790027821
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(n-k+1, k)/(n-k+1)*I^(n-k)*a136630(n, k));
A381182
E.g.f. A(x) satisfies A(x) = 1/( 1 - A(x) * sin(x * A(x)) ).
Original entry on oeis.org
1, 1, 6, 71, 1288, 31661, 984640, 37085075, 1641305472, 83497838425, 4801347029504, 307975150996831, 21802395720298496, 1688562016007776261, 142023935786330431488, 12892154760586821775019, 1256251152910271399624704, 130793914073764385411654321, 14490427167940362294881615872
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(n+2*k+1, k)/(n+2*k+1)*I^(n-k)*a136630(n, k));
Showing 1-4 of 4 results.
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