The OEIS is supported by the many generous donors to the OEIS 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 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A277406 a(n) equals the sum of all permutations of compositions of functions (1 + k*x) for k=1..n, evaluated at x=1. 3
 1, 2, 9, 76, 1100, 25176, 846132, 39321696, 2413753344, 189030205440, 18383301319680, 2172771551093760, 306662748175330560, 50933260598106862080, 9832247390118248121600, 2182733403365330313523200, 552134185815355910465126400, 157863713952139655599757721600, 50654908373638564216229105664000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..18. FORMULA a(n) = Sum_{k=0..n} k!*(n-k)! * Sum_{i=0..n-k+1} (-1)^(n-i+1) * Stirling2(i,n-k+1) * Stirling1(n+1,i)). a(n) = (n!)^2 + A277405(n). a(n) = (n+1) * A277407(n). a(n) = Sum_{k=0..n} A277408(n,k). EXAMPLE Illustration of initial terms. a(0) = 1, by convention; a(1) = 2, the function (1+x) evaluated at x=1; a(2) = 9, the sum of permutations of compositions of functions (1+x) and (1+2*x), evaluated at x=1: (1+x)o(1+2*x) + (1+2*x)o(1+x) = (2*x + 2) + (2*x + 3) = 4*x + 5. a(3) = 76, the sum of permutations of compositions of functions (1+x), (1+2*x), and (1+3*x), evaluated at x=1: (1+x)o(1+2*x)o(1+3*x) + (1+x)o(1+3*x)o(1+2*x) + (1+2*x)o(1+1*x)o(1+3*x) + (1+2*x)o(1+3*x)o(1+1*x) + (1+3*x)o(1+1*x)o(1+2*x) + (1+3*x)o(1+2*x)o(1+1*x) = (6*x + 4) + (6*x + 5) + (6*x + 5) + (6*x + 9) + (6*x + 7) + (6*x + 10) = 36*x + 40. etc. Alternatively, a(1) = 2 = Sum_{i=1..1} (1+i), a(2) = 9 = Sum_{i=1..2, j=1..2, j<>i} (1 + i*(1+j)), a(3) = 76 = Sum_{i=1..3, j=1..3, k=1..3, i,j,k distinct} (1 + i*(1 + j*(1+k))), a(4) = 1100 = Sum_{i=1..4, j=1..4, k=1..4, m=1..4, i,j,k,m distinct} (1 + i*(1 + j*(1 + k*(1+m)))), etc. MATHEMATICA Table[Sum[k!*(n-k)! * Sum[(-1)^(n-i+1) * StirlingS2[i, n-k+1] * StirlingS1[n+1, i], {i, 0, n-k+1}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 27 2016 *) PROG (PARI) {a(n) = sum(k=0, n, k!*(n-k)! * sum(i=0, n-k+1, (-1)^(n-i+1) * stirling(i, n-k+1, 2) * stirling(n+1, i, 1)))} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A277405, A277407, A277408. Sequence in context: A108992 A058164 A006059 * A182947 A006041 A192551 Adjacent sequences: A277403 A277404 A277405 * A277407 A277408 A277409 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 16 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 08:02 EST 2023. Contains 367662 sequences. (Running on oeis4.)