0,5

The a-sequence for this Sheffer matrix is A027641(n)/A027642(n) (Bernoulli numbers) and the z-sequence is A130189(n)/ A130190(n). See the W. Lang link.

Take the lower triangular matrix in A049020 and invert it, then read by rows! - N. J. A. Sloane (njas(AT)research.att.com), Feb 07 2009

Exponential Riordan array [exp(x), ln(1/(1-x))]. Equal to A007318*A132393. [From Paul Barry (pbarry(AT)wit.ie), Apr 23 2009]

W. F. Lunnon et al., Arithmetic properties of Bell numbers to a composite modulus I, Acta Arith., 35 (1979), 1-16. [From N. J. A. Sloane (njas(AT)research.att.com), Feb 07 2009]

W. Lang, First 10 rows and more.

E.g.f.: exp(t)/(1-t)^x = Sum_{n>=0} C(x,n)*t^n/n!. 1; 1, 1; 1, 3, 1; 1, 8, 6, 1; 1, 24, 29, 10, 1; ...

Sum_{k = 0..n} T(n, k)*x^k = C(x, n), Charlier polynomials; C(x, n)= A000522(n), A001339(n), A082030(n) for x = 1, 2, 3 respectively.

T(n+1, k) = (n+1)*T(n, k) + T(n, k-1) - n*T(n-1, k) with T(0, 0) = 1, T(0, k) = 0 if k>0, T(n, k) = 0 if k<0.

PS*A008275*PS as infinite lower triangular matrices, where PS is a triangle with PS[n,k] = (-1)^k*A007318[n,k]. PS = 1/PS. [From Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Aug 20 2009]

Contribution from Paul Barry (pbarry(AT)wit.ie), Apr 23 2009: (Start)

Triangle begins

1,

1, 1,

1, 3, 1,

1, 8, 6, 1,

1, 24, 29, 10, 1,

1, 89, 145, 75, 15, 1,

1, 415, 814, 545, 160, 21, 1,

1, 2372, 5243, 4179, 1575, 301, 28, 1,

1, 16072, 38618, 34860, 15659, 3836, 518, 36, 1

Production matrix is

1, 1,

0, 2, 1,

0, 1, 3, 1,

0, 1, 3, 4, 1,

0, 1, 4, 6, 5, 1,

0, 1, 5, 10, 10, 6, 1,

0, 1, 6, 15, 20, 15, 7, 1,

0, 1, 7, 21, 35, 35, 21, 8, 1,

0, 1, 8, 28, 56, 70, 56, 28, 9, 1 (End)

(PARI) {T(n, k)= local(A); if(k<0|k>n, 0, A=x*O(x^n); polcoeff( n!*polcoeff( exp(x+A)/(1-x+A)^y, n), k))} /* Michael Somos Nov 19 2006 */

Diagonals : A000012, A002104; A000012, A000217.

Row sums A000522, alternating row sums A024000.

Sequence in context: A091698 A134380 A124469 this_sequence A097712 A157210 A034801

Adjacent sequences: A094813 A094814 A094815 this_sequence A094817 A094818 A094819

nonn,tabl

DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jun 12 2004