Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
reviewed
approved
proposed
reviewed
editing
proposed
# Computes triangle as a matrix M(dim, p).
# A023531 (p=0), A056857 (p=1), this sequence (p=2), A078938 (p=3), ...
with(LinearAlgebra): M := (n, p) -> local j, k; MatrixPower(subs(exp(1) = 1,
MatrixExponential(MatrixExponential(Matrix(n, n, [seq(seq(`if`(j = k + 1, j, 0),
k = 0..n-1), j = 0..n-1)])))), p): M(8, 2); # Peter Luschny, Mar 28 2024
proposed
editing
editing
proposed
Riordan array [exp(2*exp(x)-2),x], whose production matrix has e.g.f. exp(x*t)(t+2*exp(x)). [From __Paul Barry_, Nov 26 2008]
proposed
editing
editing
proposed
1, 2, 1, 6, 4, 1, 22, 18, 6, 1, 94, 88, 36, 8, 1, 454, 470, 220, 60, 10, 1, 2430, 2724, 1410, 440, 90, 12, 1, 14214, 17010, 9534, 3290, 770, 126, 14, 1, 89918, 113712, 68050, 68040, 25424, 6580, 1232, 168, 16, 1, 610182, 809262, 511704, 204120, 57204, 11844, 1848, 216, 18, 1
Rows: {1}, {2,1}, {6,4,1}, {22,18,6,1}, {94,88,36,8,1}, {454,470,220,60,10,1}, {2430,2724,1410,440,90,12,1}, {14214,17010,9534,3290,770,126,14,1}, ...
[0] 1;
[1] 2, 1;
[2] 6, 4, 1;
[3] 22, 18, 6, 1;
[4] 94, 88, 36, 8, 1;
[5] 454, 470, 220, 60, 10, 1;
[6] 2430, 2724, 1410, 440, 90, 12, 1;
[7] 14214, 17010, 9534, 3290, 770, 126, 14, 1;
[8] 89918, 113712, 68040, 25424, 6580, 1232, 168, 16, 1;
(PARI) k=9; m=matpascal(5k)-matid(6k+1); pe=matid(6)k+m/1! + m^2/2!+m^3/3!+m^4/4!)+sum(j=15j/5j! ); A=pe^2; a(n) = A[n (sequentially read)] - _ /* _Gottfried Helms_, Apr 08 2007; amended by _Georg Fischer_ Mar 28 2024 */
a(38) corrected by Georg Fischer, Mar 28 2024
approved
editing
Riordan array [exp(2*exp(x)-2),x], whose production matrix has e.g.f. exp(x*t)(t+2*exp(x)). [From _Paul Barry (pbarry(AT)wit.ie), _, Nov 26 2008]
_Paul D. Hanna (pauldhanna(AT)juno.com), _, Dec 18 2002