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

1,2

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).

Formula

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

Example

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

Prog

(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

Crossrefs

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

Cf. A008292, A211232, A211233, A211235.

Sequence in context: A248723 A117742 A117716 * A359122 A240185 A292032

Adjacent sequences: A211231 A211232 A211233 * A211235 A211236 A211237

Keyword

sign,tabf

Author

N. J. A. Sloane, Apr 05 2012

Extensions

More terms from Franck Maminirina Ramaharo, Nov 30 2018

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

Status

approved