A384760
E.g.f. A(x) satisfies A(x) = exp( -x*A(x) * A(-x*A(x)) ).
Original entry on oeis.org
1, -1, 1, 5, -35, -281, 5671, 42671, -2179127, -9146017, 1529743051, -2876300681, -1703719191635, 19006164045023, 2748187169359087, -67807538576332801, -6002760779933693039, 267196356696377129023, 16763997717087046669459, -1258157898725874129675001
Offset: 0
E.g.f.: A(x) = 1 - x + x^2/2 + 5*x^3/6 - 35*x^4/24 - 281*x^5/120 + ...
A(x) * A(-x*A(x)) = 1 - 2*x^2/2 + 3*x^3/6 + 80*x^4/24 - 535*x^5/120 - ...
-
a(n, k=1) = if(k==0, 0^n, (-1)^n*k*sum(j=0, n, (n+k)^(j-1)*binomial(n, j)*a(n-j, j)));
A384758
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 A384757.
Original entry on oeis.org
1, 1, 0, 1, -1, 0, 1, -2, -1, 0, 1, -3, 0, 14, 0, 1, -4, 3, 34, 9, 0, 1, -5, 8, 54, -88, -1516, 0, 1, -6, 15, 68, -327, -3402, 4345, 0, 1, -7, 24, 70, -720, -4908, 30532, 507870, 0, 1, -8, 35, 54, -1255, -5044, 84321, 1027402, -4984063, 0
Offset: 0
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, -1, -2, -3, -4, -5, ...
0, -1, 0, 3, 8, 15, ...
0, 14, 34, 54, 68, 70, ...
0, 9, -88, -327, -720, -1255, ...
0, -1516, -3402, -4908, -5044, -2700, ...
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a(n, k) = if(k==0, 0^n, (-1)^n*k*sum(j=0, n, (n-j+k)^(j-1)*binomial(n, j)*a(n-j, j)));
Showing 1-2 of 2 results.