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 A144480 T(n,k) = binomial(n, k)*min(k + 1, n - k + 1), triangle read by rows (n >= 0, 0 <= k <= n). 1
 1, 1, 1, 1, 4, 1, 1, 6, 6, 1, 1, 8, 18, 8, 1, 1, 10, 30, 30, 10, 1, 1, 12, 45, 80, 45, 12, 1, 1, 14, 63, 140, 140, 63, 14, 1, 1, 16, 84, 224, 350, 224, 84, 16, 1, 1, 18, 108, 336, 630, 630, 336, 108, 18, 1, 1, 20, 135, 480, 1050, 1512, 1050, 480, 135, 20, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS FORMULA If k <= floor(n/2), then T(n,k) = binomial(n, k)*(k + 1), otherwise T(n,k) = binomial(n, k)*(n - k - 1). T(n,k) = A007318(n,k)*A003983(k+1,n-k+1), i.e., term-by term product of Pascal's triangle A007318 and A003983 as a triangle. EXAMPLE Triangle begins:   1;   1,  1;   1,  4,   1;   1,  6,   6,   1;   1,  8,  18,   8,    1;   1, 10,  30,  30,   10,    1;   1, 12,  45,  80,   45,   12,    1;   1, 14,  63, 140,  140,   63,   14,   1;   1, 16,  84, 224,  350,  224,   84,  16,   1;   1, 18, 108, 336,  630,  630,  336, 108,  18,  1;   1, 20, 135, 480, 1050, 1512, 1050, 480, 135, 20, 1;   ... MATHEMATICA Table[Table[Binomial[n, m]*If[m <= Floor[n/2], 1 + m, 1 + n - m], {m, 0, n}], {n, 0, 10}] // Flatten PROG (Maxima) create_list(binomial(n, k)*min(k + 1, n - k + 1), n, 0, 10, k, 0, n); /* Franck Maminirina Ramaharo, Dec 10 2018 */ CROSSREFS Row sums are in A245560. Cf. A003983, A007318, A168643. Sequence in context: A141540 A143188 A102413 * A144463 A174376 A131399 Adjacent sequences:  A144477 A144478 A144479 * A144481 A144482 A144483 KEYWORD nonn,easy,tabl AUTHOR Roger L. Bagula, Oct 11 2008 EXTENSIONS Entry revised by N. J. A. Sloane, Aug 07 2014 Edited by Franck Maminirina Ramaharo, Dec 10 2018 STATUS approved

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Last modified June 5 09:20 EDT 2020. Contains 334829 sequences. (Running on oeis4.)