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!)
 A174480 Rectangular array of coefficients in successive iterations of x*exp(x), as read by antidiagonals. 13
 1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 1, 4, 15, 23, 1, 1, 5, 28, 102, 104, 1, 1, 6, 45, 274, 861, 537, 1, 1, 7, 66, 575, 3400, 8598, 3100, 1, 1, 8, 91, 1041, 9425, 50734, 98547, 19693, 1, 1, 9, 120, 1708, 21216, 187455, 880312, 1270160, 136064, 1, 1, 10, 153, 2612, 41629 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Triangle A174485 forms a matrix that transforms a diagonal into an adjacent diagonal in this array. LINKS FORMULA T(n,k) = [x^k/(k-1)! ] G_{n}(x) where G_{n}(x) = G_{n-1}(x*exp(x)) with G_0(x)=x, for n>=1, k>=1. EXAMPLE Form an array of coefficients in the iterations of x*exp(x), which begin: n=1: [1, 1, 1/2!, 1/3!, 1/4!, 1/5!, 1/6!, ...]; n=2: [1, 2, 6/2!, 23/3!, 104/4!, 537/5!, 3100/6!, ...]; n=3: [1, 3, 15/2!, 102/3!, 861/4!, 8598/5!, 98547/6!, ...]; n=4: [1, 4, 28/2!, 274/3!, 3400/4!, 50734/5!, 880312/6!, ...]; n=5: [1, 5, 45/2!, 575/3!, 9425/4!, 187455/5!, 4367245/6!, ...]; n=6: [1, 6, 66/2!, 1041/3!, 21216/4!, 527631/5!, 15441636/6!, ...]; n=7: [1, 7, 91/2!, 1708/3!, 41629/4!, 1242892/5!, 43806175/6!, ...]; n=8: [1, 8, 120/2!, 2612/3!, 74096/4!, 2582028/5!, 106459312/6!, ...]; n=9: [1, 9, 153/2!, 3789/3!, 122625/4!, 4885389/5!, 230689017/6!, ...]; n=10:[1, 10, 190/2!, 5275/3!, 191800/4!, 8599285/5!, 457584940/6!,...]; ... This array begins with the above unreduced numerators for n >= 1, k >= 1. PROG (PARI) {T(n, k)=local(F=x, xEx=x*exp(x+x*O(x^(k+1)))); for(i=1, n, F=subst(F, x, xEx)); (k-1)!*polcoeff(F, k)} CROSSREFS Cf. A174485, diagonals: A174481, A174482, A174483, A174484. Cf. rows: A080108, A174493, A174494, A174495. Sequence in context: A144303 A287024 A107702 * A111670 A123353 A156540 Adjacent sequences:  A174477 A174478 A174479 * A174481 A174482 A174483 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Apr 17 2010 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 7 09:15 EST 2021. Contains 349574 sequences. (Running on oeis4.)