A384808
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where column k is the expansion of e.g.f. B(x)^k, where B(x) is the e.g.f. of A384617.
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 2, 5, 0, 1, 3, 12, 13, 0, 1, 4, 21, 56, -63, 0, 1, 5, 32, 135, 128, -2279, 0, 1, 6, 45, 256, 753, -3888, -51167, 0, 1, 7, 60, 425, 2016, -1797, -135752, -423387, 0, 1, 8, 77, 648, 4145, 8224, -224775, -2099032, 13717889, 0, 1, 9, 96, 931, 7392, 31725, -256016, -5236809, 3294432, 885044593, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 1, 2, 3, 4, 5, ...
0, 5, 12, 21, 32, 45, ...
0, 13, 56, 135, 256, 425, ...
0, -63, 128, 753, 2016, 4145, ...
0, -2279, -3888, -1797, 8224, 31725, ...
-
b(n, k) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-n+j+k)^(j-1)*binomial(n, j)*b(n-j, 2*j)));
a(n, k) = b(n, -k);
A384855
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x))^3 ).
Original entry on oeis.org
1, 1, 7, 10, -503, -8564, -103751, 3479554, 327940225, 8613464536, -36391967279, -24834942253274, -2356662167845487, -88482481533921500, 1825569695231959993, 704791058412273699106, 88829364712362626504449, 5460031123686211024338736, 23871425875449192877470625
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-n+j+k)^(j-1)*binomial(n, j)*a(n-j, 3*j)));
A384809
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^2)^2 ).
Original entry on oeis.org
1, 1, 5, 25, 153, -799, -82787, -2990343, -98020367, -2473062911, -22379003019, 3535310560409, 426542722323721, 33942691393940577, 2320589389274335117, 131491185267395291641, 4583444982950062321377, -254657491559719266483967, -86887910247671284788294683
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-2*n+2*j+k)^(j-1)*binomial(n, j)*a(n-j, 2*j)));
A384810
E.g.f. A(x) satisfies A(x) = exp( x/A(-x*A(x)^3)^2 ).
Original entry on oeis.org
1, 1, 5, 37, 417, 4761, 33313, -1509339, -135791359, -8149132943, -455269648959, -24532196772291, -1260399381304511, -56411711489070807, -1357347436103060191, 146282852689561868821, 35003916010171558562817, 5112183093788001812407521, 647998390863196992450043777
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-3*n+3*j+k)^(j-1)*binomial(n, j)*a(n-j, 2*j)));
Showing 1-4 of 4 results.