cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A198061 Array read by antidiagonals, m>=0, n>=0, A(m,n) = sum{k=0..n} sum{j=0..m} sum{i=0..m} (-1)^(j+i)*C(i,j)*n^j*k^(m-j).

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%I A198061 #8 Jul 26 2013 03:28:15
%S A198061 1,0,2,0,2,3,0,2,6,4,0,2,11,12,5,0,2,20,32,20,6,0,2,37,84,70,30,7,0,2,
%T A198061 70,224,240,130,42,8,0,2,135,612,834,550,217,56,9,0,2,264,1712,2968,
%U A198061 2354,1092,336,72,10,0,2,521,4884,10826,10310,5551,1960,492
%N A198061 Array read by antidiagonals, m>=0, n>=0, A(m,n) = sum{k=0..n} sum{j=0..m} sum{i=0..m} (-1)^(j+i)*C(i,j)*n^j*k^(m-j).
%F A198061 A198061(n,2) = A006127(n+1)
%e A198061 m\n  [0] [1]  [2]   [3]    [4]     [5]    [6]
%e A198061 ----------------------------------------------
%e A198061 [0]   1   2    3     4      5       6       7    A000027
%e A198061 [1]   0   2    6    12     20      30      42    A002378
%e A198061 [2]   0   2   11    32     70     130     217    A033994
%e A198061 [3]   0   2   20    84    240     550    1092    A098077
%e A198061 [4]   0   2   37   224    834    2354    5551
%e A198061 [5]   0   2   70   612   2968   10310   28854
%p A198061 A198061 := proc(m, n) local i,j,k,pow;
%p A198061 pow := (a,b) -> if a=0 and b=0 then 1 else a^b fi;
%p A198061 add(add(add((-1)^(j+i)*binomial(i,j)*pow(n,j)*pow(k,m-j),i=0..m),j=0..m),k=0..n) end:
%p A198061 for m from 0 to 8 do lprint(seq(A198061(m,n), n=0..6)) od;
%t A198061 Unprotect[Power]; 0^0 = 1; Protect[Power]; a[m_, n_] :=  Sum[(-1)^(j+i)*Binomial[i, j]*n^j*k^(m-j) , {i, 0, m}, {j, 0, m}, {k, 0, n}]; Table[a[m-n, n], {m, 0, 10}, {n, 0, m}] // Flatten (* _Jean-François Alcover_, Jul 26 2013 *)
%Y A198061 Cf. A198060.
%K A198061 nonn,tabl
%O A198061 0,3
%A A198061 _Peter Luschny_, Nov 02 2011