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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 February 20 09:15 EST 2019. Contains 320325 sequences. (Running on oeis4.)