The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 05:04 EDT 2021. Contains 347577 sequences. (Running on oeis4.)