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A006014 a(n+1) = (n+1)*a(n)+ Sum a(k)*a(n-k).
(Formerly M1790)
1
1, 2, 7, 32, 178, 1160, 8653, 72704, 679798, 7005632, 78939430, 965988224, 12762344596, 181108102016, 2748049240573, 44405958742016, 761423731533286, 13809530704348160 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

D. E. Knuth, personal communication.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..449

Jimmy Devillet, Bruno Teheux, Associative, idempotent, symmetric, and order-preserving operations on chains, arXiv:1805.11936 [math.RA], 2018.

FORMULA

G.f. A(x) satisfies  A(x) = x * (1 + A(x) + A(x)^2 + x * A'(x)). - Michael Somos, Jul 24 2011

EXAMPLE

x + 2*x^2 + 7*x^3 + 32*x^4 + 178*x^5 + 1160*x^6 + 8653*x^7 + 72704*x^8 + ...

MATHEMATICA

Nest[Append[#1, #1[[-1]] (#2 + 1) + Total@ Table[#1[[k]] #1[[#2 - k]], {k, #2 - 1}]] & @@ {#, Length@ #} &, {1}, 17] (* Michael De Vlieger, Aug 22 2018 *)

(* or *)

a[1] = 1; a[n_] := a[n] = n a[n-1] + Sum[a[k] a[n-1-k], {k, n-2}]; Array[a, 18] (* Giovanni Resta, Aug 23 2018 *)

PROG

(PARI) {a(n) = local(A); if( n<1, 0, A = vector(n); A[1] = 1; for( k=2, n, A[k] = k * A[k-1] + sum( j=1, k-2, A[j] * A[k-1-j])); A[n])} /* Michael Somos, Jul 24 2011 */

CROSSREFS

Sequence in context: A005362 A059439 A190123 * A121555 A265165 A301465

Adjacent sequences:  A006011 A006012 A006013 * A006015 A006016 A006017

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 12 13:46 EDT 2021. Contains 343823 sequences. (Running on oeis4.)