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 A161779 The sequence of factorials convolved with all its regularly "aerated" variants. 5
 1, 1, 3, 8, 30, 133, 768, 5221, 41302, 369170, 3677058, 40338310, 483134179, 6271796072, 87709287104, 1314511438945, 21017751750506, 357102350816602, 6424883282375340, 122025874117476166, 2439726373093186274, 51220112287152570828, 1126575412217509969515 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Essentially a duplicate of A096161: 1, followed by A096161. Convolve A000142 = 1,1,2,6,24,... with 1,0,1,0,2,0,6,0,24,.. and with 1,0,0,1,0,0,2,0,0,6,0,0,24,0,0,.. and with 1,0,0,0,1,0,0,0,2,0,0,0,6,... etc. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..449 FORMULA a(n) = A096161(n). [R. J. Mathar, Jun 26 2009] a(n) ~ n! * (1 + 1/n^2 + 2/n^3 + 7/n^4 + 28/n^5 + 121/n^6 + 587/n^7 + 3205/n^8 + 19201/n^9 + 123684/n^10), for coefficients see A293266. - Vaclav Kotesovec, Oct 04 2017 EXAMPLE Let the partial products = a, a*b, a*b*c,..., with the first few rows = (1, 1, 2, 6, 24, 120,...) = a (1, 1, 3, 7, 28, 128,...) = a*b (1, 1, 3, 8, 29, 131,...) = a*b*c (1, 1, 3, 8, 30, 132,...) = a*b*c*d ...converging to A161779 MAPLE read("transforms3") ; read("transforms") ; A161779 := proc(N) local a000142, res, n, j ; a000142 := [seq(n!, n=0..N)] ; res := [seq(op(n, a000142), n=1..N)] ; for j from 1 to N do res := CONV( res, AERATE(a000142, j)) ; od: [seq(op(n, res), n=1..N)] end: A161779(30) ; # R. J. Mathar, Jun 23 2009 # second Maple program: b:= proc(n, i) option remember;      `if`(i>n, 0, `if`(irem(n, i, 'r')=0, r!, 0)+       add(j!*b(n-i*j, i+1), j=0..n/i))     end: a:= n-> `if`(n=0, 1, b(n, 1)): seq(a(n), n=0..25);  # Alois P. Heinz, Oct 03 2018 CROSSREFS Sequence in context: A162560 A293250 A096161 * A074501 A009123 A066764 Adjacent sequences:  A161776 A161777 A161778 * A161780 A161781 A161782 KEYWORD nonn,less AUTHOR Gary W. Adamson, Jun 19 2009 EXTENSIONS Extended by R. J. Mathar, Jun 23 2009 STATUS approved

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Last modified October 20 15:07 EDT 2019. Contains 328267 sequences. (Running on oeis4.)