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Search: id:A131115
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| A131115 |
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Triangle read by rows: T(n,k)=7*binom(n,k) if k<n; T(n,n)=1 (0<=k<=n). |
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+0
6
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| 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; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums = A048489: (1, 8, 22, 50, 106, 218,...)
Non-diagonal entries of Pascal's triangle are multiplied by 7. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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FORMULA
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G.f.=G(t,z)=(1+6z-tz)/[(1-tz)(1-z-tz)]. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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EXAMPLE
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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;
...
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MAPLE
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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 (deutsch(AT)duke.poly.edu), Jun 20 2007
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CROSSREFS
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Cf. A131110, A131111, A131112, A131113, A131114, A048489, A007318.
Sequence in context: A151785 A093564 A081776 this_sequence A151778 A138616 A021937
Adjacent sequences: A131112 A131113 A131114 this_sequence A131116 A131117 A131118
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 15 2007
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EXTENSIONS
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Corrected and extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 20 2007
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