The OEIS is supported by the many generous donors to the OEIS Foundation.

 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 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A211234 Triangle read by rows: T(n,k) is the k-th generalized Eulerian number of order n and degree 4, n >= 1. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 9 13:48 EST 2023. Contains 367691 sequences. (Running on oeis4.)