A367011
a(n) = Sum_{k=0..n} k! * k^(n-k).
Original entry on oeis.org
1, 1, 3, 11, 51, 287, 1899, 14447, 124251, 1192127, 12623979, 146250287, 1840024251, 24983863967, 364140992139, 5670546353807, 93960923507931, 1650688221777407, 30646388716777899, 599565840087487727, 12328458398407260411
Offset: 0
-
Table[Sum[k! * k^(n-k), {k, 0, n}], {n, 1, 20}]
-
a(n) = sum(k=0, n, k!*k^(n-k)); \\ Seiichi Manyama, Dec 31 2023
A368555
a(n) = Sum_{k=0..n} k! * 3^(n-k).
Original entry on oeis.org
1, 4, 14, 48, 168, 624, 2592, 12816, 78768, 599184, 5426352, 56195856, 647589168, 8169788304, 111687656112, 1642737336336, 25851001897008, 433240433787024, 7702095007089072, 144751385430099216, 2867156164466937648, 59692410665110252944
Offset: 0
A361042
Triangle read by rows: T(n, k) = Sum_{j=0..n} j! * binomial(n - j, n - k).
Original entry on oeis.org
1, 1, 2, 1, 3, 4, 1, 4, 7, 10, 1, 5, 11, 17, 34, 1, 6, 16, 28, 51, 154, 1, 7, 22, 44, 79, 205, 874, 1, 8, 29, 66, 123, 284, 1079, 5914, 1, 9, 37, 95, 189, 407, 1363, 6993, 46234, 1, 10, 46, 132, 284, 596, 1770, 8356, 53227, 409114, 1, 11, 56, 178, 416, 880, 2366, 10126, 61583, 462341, 4037914
Offset: 0
Triangle T(n, k) starts:
[0] 1;
[1] 1, 2;
[2] 1, 3, 4;
[3] 1, 4, 7, 10;
[4] 1, 5, 11, 17, 34;
[5] 1, 6, 16, 28, 51, 154;
[6] 1, 7, 22, 44, 79, 205, 874;
[7] 1, 8, 29, 66, 123, 284, 1079, 5914;
[8] 1, 9, 37, 95, 189, 407, 1363, 6993, 46234;
[9] 1, 10, 46, 132, 284, 596, 1770, 8356, 53227, 409114.
Showing 1-3 of 3 results.