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 A277176 Exponential convolution of Catalan numbers and factorial numbers. 3
 1, 2, 6, 23, 106, 572, 3564, 25377, 204446, 1844876, 18465556, 203179902, 2438366836, 31699511768, 443795839192, 6656947282725, 106511191881270, 1810690391626380, 32592427526913540, 619256124778620450, 12385122502136529420, 260087572569333384840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) = number of permutations of [n+1] in which the first entry does not start a (classical) 1234 pattern. The number of such permutations with first entry i is n!/(n + 1 - i)! C(n + 1 - i) where C(n) is the Catalan number A000108(n). - David Callan, Jun 12 2017 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..449 FORMULA E.g.f.: exp(2*x)/(1-x)*(BesselI(0,2*x)-BesselI(1,2*x)). a(n) = Sum_{i=0..n} binomial(n,i) * C(i) * (n-i)!. a(n) ~ exp(2) * BesselI(2,2) * n!. - Vaclav Kotesovec, Oct 13 2016 MAPLE a:= proc(n) option remember; `if`(n<2, n+1,      ((n^2+5*n-2)*a(n-1)-(4*n-2)*(n-1)*a(n-2))/(n+1))     end: seq(a(n), n=0..30); CROSSREFS Cf. A000108, A000142, A277175, A277359. Sequence in context: A263780 A125273 A187761 * A130908 A200404 A000772 Adjacent sequences:  A277173 A277174 A277175 * A277177 A277178 A277179 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 02 2016 STATUS approved

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Last modified October 16 13:51 EDT 2019. Contains 328093 sequences. (Running on oeis4.)