A244143 Triangle read by rows: terms T(n,k) of a binomial decomposition of n as Sum(k=0..n)T(n,k).

0, 0, 1, 0, 0, 2, 0, 0, 18, -15, 0, 0, 108, -300, 196, 0, 0, 540, -3750, 6860, -3645, 0, 0, 2430, -37500, 144060, -196830, 87846, 0, 0, 10206, -328125, 2352980, -6200145, 6764142, -2599051, 0, 0, 40824, -2625000, 32941720, -148803480, 297622248, -270301304, 91125000

Offset

0,6

Comments

T(n,k)=(-1)^k*k*(2*k-1)^(n-2)*binomial(n,k) for k>1, while T(n,0)=0 and T(1,1)=0^(n-1) by convention.

Links

Stanislav Sykora, Table of n, a(n) for rows 0..100

S. Sykora, An Abel's Identity and its Corollaries, Stan's Library, Volume V, 2014, DOI 10.3247/SL5Math14.004. See eq.(21), with a=1, b=2.

Example

First rows of the triangle, all summing up to n:
0,
0, 1,
0, 0, 2,
0, 0, 18, -15,
0, 0, 108, -300, 196,
0, 0, 540, -3750, 6860, -3645,

Prog

(PARI) seq(nmax)={my(v, n, k, irow);
v = vector((nmax+1)*(nmax+2)/2); v[1]=0;
for(n=1, nmax, irow=1+n*(n+1)/2;
  v[irow]=0; if(n==1, v[irow+1]=1, v[irow+1]=0);
for(k=2, n, v[irow+k]=(-1)^k*k*(2*k-1)^(n-2)*binomial(n, k); ); );
return(v); }
a=seq(100);

Crossrefs

Cf. A244116, A244117, A244118, A244119, A244120, A244121, A244122, A244123, A244124, A244125, A244126, A244127, A244128, A244129, A244130, A244131, A244132, A244133, A244134, A244135, A244136, A244137, A244138, A244139, A244140, A244141, A244142.

Sequence in context: A120582 A003784 A368849 * A066294 A363073 A230840

Adjacent sequences: A244140 A244141 A244142 * A244144 A244145 A244146

Keyword

sign,tabl

Author

Stanislav Sykora, Jun 23 2014

Status

approved