A385058
E.g.f. A(x) satisfies A(x) = exp(x*A(x)/A(-x*A(x))).
Original entry on oeis.org
1, 1, 5, 31, 333, 3841, 57463, 836109, 11138921, 14908465, -10091931669, -687827361011, -40151825312387, -2071761364164231, -106488772704576961, -5002145237145820979, -203989286928198178863, -4164191357488024315679, 500440079223957671460307, 99906607739361143393212941
Offset: 0
-
a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, (-n+k)^(j-1)*binomial(n, j)*a(n-j, j)));
A181320
Triangle T(n,m) read by rows: the number of series-parallel networks with n+2 vertices and m+n+1 edges.
Original entry on oeis.org
1, 1, 1, 2, 7, 5, 6, 48, 91, 49, 24, 360, 1304, 1697, 729, 120, 3000, 17910, 41440, 41051, 14641, 720, 27720, 249900, 899730, 1524282, 1218745, 371293
Offset: 0
The table d_(n,m) [which is T(n,m) with leading zeros maintained] for the number of SP networks with n+2 vertices and m nodes (internal nodes labeled from 1 to n) starts in row n=0 with columns m>=0 as:
n\m| 0 1 2 3 4
----------------------
0 | 0 1
1 | 0 0 1 1
2 | 0 0 0 2 7 5
3 | 0 0 0 0 6 48 91 49
A364870
Array read by ascending antidiagonals: A(n, k) = (n + k)^n, with k >= 0.
Original entry on oeis.org
1, 1, 1, 4, 2, 1, 27, 9, 3, 1, 256, 64, 16, 4, 1, 3125, 625, 125, 25, 5, 1, 46656, 7776, 1296, 216, 36, 6, 1, 823543, 117649, 16807, 2401, 343, 49, 7, 1, 16777216, 2097152, 262144, 32768, 4096, 512, 64, 8, 1, 387420489, 43046721, 4782969, 531441, 59049, 6561, 729, 81, 9, 1
Offset: 0
The array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, ...
4, 9, 16, 25, 36, 49, ...
27, 64, 125, 216, 343, 512, ...
256, 625, 1296, 2401, 4096, 6561, ...
3125, 7776, 16807, 32768, 59049, 100000, ...
...
Cf.
A000012 (n=0),
A000169,
A000272,
A000312 (k=0),
A007830 (k=3),
A008785 (k=4),
A008786 (k=5),
A008787 (k=6),
A031973 (antidiagonal sums),
A052746 (2nd superdiagonal),
A052750,
A062971 (main diagonal),
A079901 (read by descending antidiagonals),
A085527 (1st superdiagonal),
A085528 (1st subdiagonal),
A085532,
A099753.
-
A[n_,k_]:=(n+k)^n; Join[{1},Table[A[n-k,k],{n,9},{k,0,n}]]//Flatten
Comments