A381442
Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + sinh(x))^2 ).
Original entry on oeis.org
1, 2, 10, 86, 1080, 18042, 377936, 9538622, 281946496, 9557102450, 365548361472, 15576454300134, 731807446707200, 37584596599753322, 2094995668172597248, 125966553940498047182, 8127048592610380578816, 560040497770823162810082, 41054563701320694564061184
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+2, k)*a136630(n, k))/(n+1);
A381430
E.g.f. A(x) satisfies A(x) = 1 + sinh(x*A(x)^3).
Original entry on oeis.org
1, 1, 6, 73, 1368, 34861, 1126368, 44135701, 2034072960, 107823563641, 6463383851520, 432331180935457, 31924171503581184, 2579483385868484005, 226383845487041421312, 21445302563389991287981, 2180974075392495296544768, 237009522316557393020262001, 27409082977094100068471537664
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(3*n+1, k)*a136630(n, k))/(3*n+1);
A381518
Expansion of e.g.f. ( (1/x) * Series_Reversion( x/(1 + sin(x))^2 ) )^(1/2).
Original entry on oeis.org
1, 1, 4, 29, 304, 4141, 68832, 1337881, 29432576, 712263961, 18403873280, 487814777141, 12296236382208, 230142147098501, -2906327530115072, -800177574047914831, -75835523291585773568, -6054072134316123116495, -459749417224473755910144, -34556942957229166465685555
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+1, k)*I^(n-k)*a136630(n, k))/(2*n+1);
Showing 1-3 of 3 results.