OFFSET
0,6
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
EXAMPLE
T(3,2) = 9: aaaabb, aaabba, aabaab, aabbaa, aabbbb, abaaba, abbaaa, abbabb, abbbba.
T(3,3) = 10: aabbcc, aabccb, aacbbc, aaccbb, abbacc, abbcca, abccba, acbbca, accabb, accbba.
T(4,2) = 34: aaaaaabb, aaaaabba, aaaabaab, aaaabbaa, aaaabbbb, aaabaaba, aaabbaaa, aaabbabb, aaabbbba, aabaaaab, aabaabaa, aabaabbb, aababbab, aabbaaaa, aabbaabb, aabbabba, aabbbaab, aabbbbaa, aabbbbbb, abaaaaba, abaabaaa, abaababb, abaabbba, ababbaba, abbaaaaa, abbaaabb, abbaabba, abbabaab, abbabbaa, abbabbbb, abbbaaba, abbbbaaa, abbbbabb, abbbbbba.
T(4,4) = 84: aabbccdd, aabbcddc, aabbdccd, aabbddcc, aabccbdd, aabccddb, aabcddcb, aabdccdb, aabddbcc, aabddccb, aacbbcdd, aacbbddc, aacbddbc, aaccbbdd, aaccbddb, aaccdbbd, aaccddbb, aacdbbdc, aacddbbc, aacddcbb, aadbbccd, aadbbdcc, aadbccbd, aadcbbcd, aadccbbd, aadccdbb, aaddbbcc, aaddbccb, aaddcbbc, aaddccbb, abbaccdd, abbacddc, abbadccd, abbaddcc, abbccadd, abbccdda, abbcddca, abbdccda, abbddacc, abbddcca, abccbadd, abccbdda, abccddba, abcddcba, abdccdba, abddbacc, abddbcca, abddccba, acbbcadd, acbbcdda, acbbddca, acbddbca, accabbdd, accabddb, accadbbd, accaddbb, accbbadd, accbbdda, accbddba, accdbbda, accddabb, accddbba, acdbbdca, acddbbca, acddcabb, acddcbba, adbbccda, adbbdacc, adbbdcca, adbccbda, adcbbcda, adccbbda, adccdabb, adccdbba, addabbcc, addabccb, addacbbc, addaccbb, addbbacc, addbbcca, addbccba, addcbbca, addccabb, addccbba.
Triangle T(n,k) begins:
1;
0, 1;
0, 1, 2;
0, 1, 9, 10;
0, 1, 34, 112, 84;
0, 1, 125, 930, 1800, 1008;
0, 1, 461, 7018, 26400, 35640, 15840;
0, 1, 1715, 51142, 334152, 816816, 840840, 308880;
MAPLE
A:= proc(n, k) option remember; `if`(n=0, 1, k/n*
add(binomial(2*n, j) *(n-j) *(k-1)^j, j=0..n-1))
end:
T:= (n, k)-> add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)/
`if`(k=0, 1, k):
seq(seq(T(n, k), k=0..n), n=0..12);
MATHEMATICA
Unprotect[Power]; 0^0 = 1; A[n_, k_] := A[n, k] = If[n==0, 1, k/n*Sum[ Binomial[2*n, j]*(n-j)*(k-1)^j, {j, 0, n-1}]];
T[n_, k_] := Sum[A[n, k-i]*(-1)^i*Binomial[k, i], {i, 0, k}]/If[k==0, 1, k]; Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Feb 22 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Mar 15 2015
STATUS
approved