A382851 a(n) = least number in row n of Pascal's triangle that exceeds every number in row n-1.
2, 3, 4, 10, 15, 21, 56, 84, 210, 330, 495, 1287, 2002, 5005, 8008, 19448, 31824, 50388, 125970, 203490, 497420, 817190, 1961256, 3268760, 5311735, 13037895, 21474180, 51895935, 86493225, 206253075, 347373600, 818809200, 1391975640, 3247943160, 5567902560
Offset: 2
Keywords
Examples
Rows 0 to 5 of Pascal's triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1,
10 is the least number in row 5 that exceeds max{1,4,6}, so a(5)=10
Programs
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Mathematica
z = 40; c[n_, k_] := Binomial[n, k]; t[n_] := Table[c[n, k], {k, 0, n}]; a[n_] := Select[Range[z], c[n, #] > c[n - 1, Floor[(n - 1)/2]] &, 1]; Flatten[Table[a[n], {n, 1, 3 z}]] (* A382850 *) Flatten[Table[c[n, a[n]], {n, 1, z}]] (* A382851 *) a[n_] := Block[{b, k = 1, m = Binomial[n -1, Floor[(n -1)/2]]}, While[b = Binomial[n, k]; b < m, k++]; b]; Array[a, 35, 2] (* Robert G. Wilson v, May 02 2025 *) -
PARI
row(n) = vector(n+1, k, binomial(n,k-1)); a(n) = my(val = vecmax(row(n-1)), w = row(n)); for (i=1, #w, if (w[i] > val, return(w[i]));); \\ Michel Marcus, Apr 13 2025