A172040
Triangle T(n,k), read by rows, given by [0,1,2,1,2,1,2,1,2,1,2,...] DELTA [2,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
Original entry on oeis.org
1, 0, 2, 0, 2, 4, 0, 6, 8, 8, 0, 22, 28, 24, 16, 0, 90, 112, 96, 64, 32, 0, 394, 484, 416, 288, 160, 64, 0, 1806, 2200, 1896, 1344, 800, 384, 128, 0, 8558, 10364, 8952, 6448, 4000, 2112, 896, 256, 0, 41586, 50144, 43392, 31616, 20160, 11264, 5376, 2048, 512, 0
Offset: 0
Triangle begins:
1 ;
0,2 ;
0,2,4 ;
0,6,8,8 ;
0,22,28,24,16 ; ...
A183875
Triangle T(n,k) for A(x)^k=sum(n>=k T(n,k)*x^n), where o.g.f. A(x) satisfies A(x)=(a+b*x*A(x))/(c-d*x*A(x)), a=1,b=2,c=1,d=2.
Original entry on oeis.org
1, 4, 1, 24, 8, 1, 176, 64, 12, 1, 1440, 544, 120, 16, 1, 12608, 4864, 1168, 192, 20, 1, 115584, 45184, 11424, 2112, 280, 24, 1, 1095424, 432128, 113088, 22528, 3440, 384, 28, 1, 10646016, 4227584, 1133952, 237824, 39840, 5216, 504, 32, 1, 105522176, 42115072, 11506944, 2505728, 448064, 65280, 7504, 640, 36, 1
Offset: 1
1,
4,1,
24,8,1,
176,64,12,1,
1440,544,120,16,1,
12608,4864,1168,192,20,1,
115584,45184,11424,2112,280,24,1,
1095424,432128,113088,22528,3440,384,28,1,
10646016,4227584,1133952,237824,39840,5216,504,32,1,
105522176,42115072,11506944,2505728,448064,65280,7504,640,36,1
-
T[n_, k_, a_, b_, c_, d_] := k/n Sum[Binomial[n, n - k - i] a^(k + i) b^(n - k - i) Binomial[i + n - 1, n - 1] c^(-i - n) d^i, {i, 0, n - k}];
T[n_, k_] := T[n, k, 1, 2, 1, 2];
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Aug 08 2018, from formula *)
Showing 1-2 of 2 results.
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