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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A341014 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Sum_{j=0..n} k^j * j! * binomial(n,j)^2. 5
 1, 1, 1, 1, 2, 1, 1, 3, 7, 1, 1, 4, 17, 34, 1, 1, 5, 31, 139, 209, 1, 1, 6, 49, 352, 1473, 1546, 1, 1, 7, 71, 709, 5233, 19091, 13327, 1, 1, 8, 97, 1246, 13505, 95836, 291793, 130922, 1, 1, 9, 127, 1999, 28881, 318181, 2080999, 5129307, 1441729, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Seiichi Manyama, Antidiagonals n = 0..139, flattened FORMULA E.g.f. of column k: exp(x/(1-k*x)) / (1-k*x). T(n,k) = (2*k*n-k+1) * T(n-1,k) - k^2 * (n-1)^2 * T(n-2,k) for n > 1. EXAMPLE Square array begins:   1,    1,     1,     1,      1,      1, ...   1,    2,     3,     4,      5,      6, ...   1,    7,    17,    31,     49,     71, ...   1,   34,   139,   352,    709,   1246, ...   1,  209,  1473,  5233,  13505,  28881, ...   1, 1546, 19091, 95836, 318181, 830126, ... MATHEMATICA T[n_, k_] := Sum[If[j == k == 0, 1, k^j]*j!*Binomial[n, j]^2, {j, 0, n}]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, Feb 02 2021 *) PROG (PARI) {T(n, k) = sum(j=0, n, k^j*j!*binomial(n, j)^2)} CROSSREFS Columns 0..4 give A000012, A002720, A025167, A102757, A102773. Rows 0..2 give A000012, A000027(n+1), A056220(n+1). Main diagonal gives A330260. Cf. A307883. Sequence in context: A163181 A074662 A025243 * A145085 A228904 A144512 Adjacent sequences:  A341011 A341012 A341013 * A341015 A341016 A341017 KEYWORD nonn,tabl AUTHOR Seiichi Manyama, Feb 02 2021 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 November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)