This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A093905 Triangle read by rows: for 0 <= k < n, a(n, k) is the sum of the products of all subsets of {n-k, n-k+1, ..., n} with k members. 6
 1, 1, 3, 1, 5, 11, 1, 7, 26, 50, 1, 9, 47, 154, 274, 1, 11, 74, 342, 1044, 1764, 1, 13, 107, 638, 2754, 8028, 13068, 1, 15, 146, 1066, 5944, 24552, 69264, 109584, 1, 17, 191, 1650, 11274, 60216, 241128, 663696, 1026576, 1, 19, 242, 2414, 19524, 127860 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Triangle A165674, which is the reversal of this triangle, is generated by the asymptotic expansion of the higher order exponential integral E(x,m=2,n). - Johannes W. Meijer, Oct 16 2009 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA a(n, k) = (Product_{i=n-k..n} i)*(Sum_{i=n-k..n} 1/i), where a(n, 0) = 1. a(n, k) = A067176(n, n-k-1) = A105954(k+1, n-k). Row sums are given by A093344. EXAMPLE Triangle begins: 1 1 3 1 5 11 1 7 26 50 1 9 47 154 274 ... a(5, 3) = 4*3*2+5*3*2+5*4*2+5*4*3 = 154. MATHEMATICA T[n_, 0] := 1; T[n_, k_]:= Product[i, {i, n - k, n}]*Sum[1/i, {i, n - k, n}]; Table[T[n, k], {n, 1, 10}, {k, 0, n - 1}] (* G. C. Greubel, Jan 21 2017 *) PROG (PARI) a(n, k) = prod(i=n-k, n, i)*sum(i=n-k, n, 1/i); tabl(nn) = for (n=1, nn, for (k=0, n-1, print1(a(n, k), ", ")); print()); \\ Michel Marcus, Jan 21 2017 CROSSREFS The leading diagonal is given by A000254, Stirling numbers of first kind. The next nine diagonals are A001705, A001711, A001716, A001721, A051524, A051545, A051560, A051562 and A051564, generalized Stirling numbers. Cf. A001705, A001711, A067176, A093344, A105954. A165674 is the reversal of this triangle. - Johannes W. Meijer, Oct 16 2009 Sequence in context: A233037 A275999 A286910 * A324017 A063853 A219078 Adjacent sequences:  A093902 A093903 A093904 * A093906 A093907 A093908 KEYWORD nonn,easy,tabl AUTHOR Amarnath Murthy, Apr 24 2004 EXTENSIONS Edited and extended by David Wasserman, Apr 24 2007 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 December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)