A211234 Triangle read by rows: T(n,k) is the k-th generalized Eulerian number of order n and degree 4, n >= 1.

1, 2, 3, 4, 1, 4, 10, 20, 10, 4, 1, 1, 7, 27, 77, 57, 0, -57, -77, -27, -7, -1, 1, 12, 69, 272, 221, -272, -1084, -1688, -1084, -272, 221, 272, 69, 12, 1, 1, 21, 176, 936, 625, -3288, -11868, -21023, -16223, 0, 16223, 21023, 11868, 3288, -625, -936, -176, -21, -1

Offset: 1

Author

N. J. A. Sloane, Apr 05 2012

Keywords

• sign
• tabf

Examples

			Triangle begins:
  1, 2,  3,  4;
  1, 4, 10, 20, 10, 4,   1;
  1, 7, 27, 77, 57, 0, -57, -77, -27, -7, -1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1276 (rows 1..25)
• D. H. Lehmer, Generalized Eulerian numbers, J. Combin. Theory Ser.A 32 (1982), no. 2, 195-215. MR0654621 (83k:10026).

Crossrefs

Row sums of even rows are A047683; row sums of odd rows are zero for n > 1.

Cf. A008292, A211232, A211233, A211235.

Programs

PARI

T(n,r=4)={my(R=vector(n)); R[1]=[1..r]; for(n=2, n, my(u=R[n-1]); R[n]=vector(r*n-1, k, sum(j=0, r, (k - j*n)*if(k>j && k-j<=#u, u[k-j], 0)))); R}
{ my(A=T(5)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, May 18 2020

Formula

A047683(n) = Sum_{k>=1} T(2*n, k). - Andrew Howroyd, May 18 2020

Extensions

More terms from Franck Maminirina Ramaharo, Nov 30 2018

a(20) corrected by Andrew Howroyd, May 18 2020