cp's OEIS Frontend

A177429 Triangle read by rows: T(n,m)=A060187(1+n,1+m) *n! / (n-m)!

%I A177429 #5 Jun 17 2015 04:14:11
%S A177429 1,1,1,1,12,2,1,69,138,6,1,304,2760,1824,24,1,1185,33640,100920,28440,
%T A177429 120,1,4332,316290,2825760,3795480,519840,720,1,15253,2547594,
%U A177429 54541830,218167320,152855640,10982160,5040,1,52416,18570272,835056768
%N A177429 Triangle read by rows: T(n,m)=A060187(1+n,1+m) *n! / (n-m)!
%C A177429 Row sums are: 1, 2, 15, 214, 4913, 164306, 7462423, 439114838, 32358353217, 2909210035042, 312597121198751,...
%e A177429 1;
%e A177429 1, 1;
%e A177429 1, 12, 2;
%e A177429 1, 69, 138, 6;
%e A177429 1, 304, 2760, 1824, 24;
%e A177429 1, 1185, 33640, 100920, 28440, 120;
%e A177429 1, 4332, 316290, 2825760, 3795480, 519840, 720;
%e A177429 1, 15253, 2547594, 54541830, 218167320, 152855640, 10982160, 5040;
%e A177429 1, 52416, 18570272, 835056768, 7854023520, 16701135360, 6685297920, 264176640, 40320;
%e A177429 1, 177057, 126456480, 10940817888, 209905801056, 1049529005280, 1312898146560, 318670329600, 7138938240, 362880;
%p A177429 A177429 := proc(n,k)
%p A177429     A060187(n+1,k+1)*n!/(n-k)! ;
%p A177429 end proc: # _R. J. Mathar_, Jun 16 2015
%t A177429 (*A060187*);
%t A177429 p[x_, n_] = (1 - x)^(n + 1)*Sum[(2*k + 1)^n*x^k, {k, 0, Infinity}];
%t A177429 f[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];
%t A177429 t[n_, m_] := f[n, m]*n!/(n - m)!;
%t A177429 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A177429 Flatten[%]
%Y A177429 Cf. A060187
%K A177429 nonn,tabl,easy
%O A177429 0,5
%A A177429 _Roger L. Bagula_, May 08 2010