The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A262886 Regular triangle read by rows: T(n, k) = sum(i=0, n, sum(j=k, n, 3*(-1)^(k+j)*binomial(2*k,k)*binomial(j,i)*binomial(n,i)*binomial(i,n-j)/(2*(2*i-1)*(2*j+1)*(2*n-2*i-1)))). 0
 -2, 0, 6, 0, 0, 24, 0, 0, 4, 118, 0, 0, 0, 60, 696, 0, 0, 0, 12, 720, 4824, 0, 0, 0, 0, 336, 8288, 38240, 0, 0, 0, 0, 60, 6516, 95928, 336822, 0, 0, 0, 0, 0, 2520, 109872, 1131732, 3215544, 0, 0, 0, 0, 0, 392, 67904, 1735320, 13647840, 32651544 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS MathOverflow, How to prove this polynomial always has integer values at all integers?, Jun 13 2015. Wilberd van der Kallen, How to prove this polynomial always has integer values at all integers, arXiv:1509.08811 [math.NT], 2015. FORMULA T(0, 0) = 3/2, so sequence here as offset 1. T(n, k) = 0 for k>n, so only the terms with k<=n are represented here. EXAMPLE Triangle starts: -2; 0, 6; 0, 0, 24; 0, 0, 4, 118; 0, 0, 0, 60, 696; 0, 0, 0, 12, 720, 4824; 0, 0, 0, 0, 336, 8288, 38240; 0, 0, 0, 0, 60, 6516, 95928, 336822; ... MATHEMATICA Table[Sum[Sum[3 (-1)^(k + j) Binomial[2 k, k] Binomial[j, i] Binomial[n, i] Binomial[i, n - j]/(2 (2 i - 1) (2 j + 1) (2 n - 2 i - 1)), {j, k, n}], {i, 0, n}], {n, 10}, {k, n}] // Flatten (* Michael De Vlieger, Oct 04 2015 *) PROG (PARI) d(n, k) = sum(i=0, n, sum(j=k, n, 3*(-1)^(k+j)*binomial(2*k, k)*binomial(j, i)*binomial(n, i)*binomial(i, n-j)/(2*(2*i-1)*(2*j+1)*(2*n-2*i-1)))); tabl(nn) = {for (n=1, nn, for (k=1, n, print1(d(n, k), ", "); ); print(); ); } CROSSREFS Sequence in context: A047918 A321981 A322481 * A138701 A332400 A274878 Adjacent sequences:  A262883 A262884 A262885 * A262887 A262888 A262889 KEYWORD sign,tabl AUTHOR Michel Marcus, Oct 04 2015 STATUS approved

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

Last modified September 21 22:33 EDT 2020. Contains 337274 sequences. (Running on oeis4.)