This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A109822 Triangle read by rows: T(n,1)=1, T(n,k) = T(n-1,k) + (n-1)T(n-1, k-1) for 1 <= k <= n. 2
 1, 1, 2, 1, 4, 6, 1, 7, 18, 24, 1, 11, 46, 96, 120, 1, 16, 101, 326, 600, 720, 1, 22, 197, 932, 2556, 4320, 5040, 1, 29, 351, 2311, 9080, 22212, 35280, 40320, 1, 37, 583, 5119, 27568, 94852, 212976, 322560, 362880, 1, 46, 916, 10366, 73639, 342964, 1066644 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS T(n,n) = n!. Sum of row n is the signless Stirling number of the first kind s(n,2)(A000254). T(n,k) = A096747(n,k) for 1 <= k <= n. LINKS FORMULA T(n, k) = Sum_{i=0..k-1} |stirling1(n, n-i)| for 1 <= k <= n. From Peter Bala, Jul 08 2012: (Start) E.g.f.: x/(1-x)*{1/(1-x*z)^(1/x) - 1/(1-x*z)} = x*z + (x + 2*x^2)*z^2/2! + (x + 4*x^2 + 6*x^3)*z^3/3! + ... Cf. the e.g.f. of A059518. (End) EXAMPLE T(5,3) = 46 because 18 + 4*7 = 46. Triangle begins: Row 1:                    1 Row 2:                 1     2 Row 3:              1     4     6 Row 4:           1     7    18    24 Row 5:        1    11    46    96   120 Row 6:     1    16   101   326   600   720 Row 7:  1    22   197   932  2556  4320  5040 MAPLE with(combinat): T:=(n, k)->add(abs(stirling1(n, n-i)), i=0..k-1): for n from 1 to 11 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form T:=proc(n, k) if k=1 then 1 elif k=n then n! else T(n-1, k)+(n-1)*T(n-1, k-1) fi end: for n from 1 to 11 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form. - Emeric Deutsch, Jul 03 2005 A109822_row := proc(n) local k, i; add(add(abs(combinat[stirling1](n, n-i)), i=0..k)*x^(n-k-1), k=0..n-1); seq(coeff(%, x, n-k), k=1..n) end: seq(print(A109822_row(n)), n=1..7); # Peter Luschny, Sep 18 2011 MATHEMATICA Table[Sum[Abs@ StirlingS1[n, n - i], {i, 0, k - 1}], {n, 10}, {k, n}] // Flatten (* Michael De Vlieger, Aug 17 2017 *) CROSSREFS Cf. A000254, A049444, A059518, A096747, A137650. Sequence in context: A219142 A220226 A181854 * A274292 A114192 A114656 Adjacent sequences:  A109819 A109820 A109821 * A109823 A109824 A109825 KEYWORD nonn,tabl AUTHOR Emeric Deutsch, Jul 03 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.