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);
A381175
E.g.f. A(x) satisfies A(x) = 1/( 1 - x * A(x)^2 * cos(x * A(x)) ).
Original entry on oeis.org
1, 1, 6, 69, 1224, 29465, 898320, 33187133, 1441200768, 71956238769, 4061414246400, 255737764687669, 17773804761259008, 1351494159065894857, 111608708333568036864, 9947544079380663728685, 951770403836914402099200, 97301151510219112917218657, 10585077723403580668983902208
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+2*k+1, k)/(n+2*k+1)*I^(n-k)*a185951(n, k));
A381181
Expansion of e.g.f. (1/x) * Series_Reversion( x / (1 + sin(x)) ).
Original entry on oeis.org
1, 1, 2, 5, 8, -79, -1584, -20539, -223616, -1855295, -1736960, 435730789, 14511117312, 338965239601, 6202042886144, 71638247035109, -714560796196864, -84697775518956799, -3650903032332091392, -115829159202293866939, -2739961030150105333760, -29414406825401517785039
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+1, k)*I^(n-k)*a136630(n, k))/(n+1);
A381174
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x*cos(x)) ).
Original entry on oeis.org
1, 1, 4, 27, 264, 3365, 52800, 980903, 20984320, 506078505, 13525493760, 394758794419, 12414039171072, 414990179398093, 14523823020621824, 521523225315049215, 18594912994237808640, 613842569215361446097, 14735570097970682265600, -228398321523777856462261
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+k+1, k)/(n+k+1)*I^(n-k)*a185951(n, k));
A381176
E.g.f. A(x) satisfies A(x) = 1 + x*cos(x*A(x)).
Original entry on oeis.org
1, 1, 0, -3, -24, -55, 480, 8813, 61824, -264591, -13662720, -185252771, -117427200, 52162650553, 1214778679296, 7998339208845, -370278535495680, -14623177924271263, -202753399336206336, 3863010744775239101, 286065782789626920960, 6603193175290504771881
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-k+1, k)/(n-k+1)*I^(n-k)*a185951(n, k));
Showing 1-5 of 5 results.
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