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 A131115 Triangle read by rows: T(n,k) = 7*binomial(n,k) with T(n,n)=1. 7
 1, 7, 1, 7, 14, 1, 7, 21, 21, 1, 7, 28, 42, 28, 1, 7, 35, 70, 70, 35, 1, 7, 42, 105, 140, 105, 42, 1, 7, 49, 147, 245, 245, 147, 49, 1, 7, 56, 196, 392, 490, 392, 196, 56, 1, 7, 63, 252, 588, 882, 882, 588, 252, 63, 1, 7, 70, 315, 840, 1470, 1764, 1470, 840, 315, 70, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums give A048489. Non-diagonal entries of Pascal's triangle are multiplied by 7. - Emeric Deutsch, Jun 20 2007 The matrix inverse starts             1;            -7,         1;            91,       -14,         1;         -1771,       273,       -21,       1;         45955,     -7084,       546,     -28,      1;      -1490587,    229775,    -17710,     910,    -35,    1;      58018051,  -8943522,    689325,  -35420,   1365,  -42,   1;   -2634606331, 406126357, -31302327, 1608425, -61985, 1911, -49, 1; - R. J. Mathar, Mar 15 2013 LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened FORMULA G.f.: (1 + 6*x - t*x)/((1-t*x)*(1-x-t*x)). - Emeric Deutsch, Jun 20 2007 EXAMPLE First few rows of the triangle are:   1;   7,  1;   7, 14,  1;   7, 21, 21,  1;   7, 28, 42, 28,  1;   7, 35, 70, 70, 35, 1; ... MAPLE T := proc (n, k) if k < n then 7*binomial(n, k) elif k = n then 1 else 0 end if end proc; for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jun 20 2007 MATHEMATICA Table[If[k==n, 1, 7*Binomial[n, k]], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 18 2019 *) PROG (PARI) T(n, k)=if(k==n, 1, 7*binomial(n, k)) \\ Charles R Greathouse IV, Jan 16 2012 (MAGMA) [k eq n select 1 else 7*Binomial(n, k): k in [0..n], n in [0..10]]; // G. C. Greubel, Nov 18 2019 (Sage) @CachedFunction def T(n, k):     if (k==n): return 1     else: return 7*binomial(n, k) [[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 18 2019 (GAP) T:= function(n, k)     if k=n then return 1;     else return 7*Binomial(n, k);     fi;  end; Flat(List([0..10], n-> List([0..n], k-> T(n, k) ))); # G. C. Greubel, Nov 18 2019 CROSSREFS Cf. A007318, A048489, A131110, A131111, A131112, A131113, A131114. Sequence in context: A093564 A081776 A256255 * A151778 A138616 A021937 Adjacent sequences:  A131112 A131113 A131114 * A131116 A131117 A131118 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Jun 15 2007 EXTENSIONS Corrected and extended by Emeric Deutsch, Jun 20 2007 STATUS approved

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Last modified January 25 19:09 EST 2020. Contains 331249 sequences. (Running on oeis4.)