A290581 - OEIS

%I #8 Aug 21 2017 17:29:10

%S 1,20,364,7028,148752,3471192,89097664,2503362488,76575071488,

%T 2536513162508,90532686154752,3465845396598540,141726054915248128,

%U 6167370619705004144,284635248765764878336,13889365886508877963184,714612366728939248091136,38667882915659893417754820,2195406208657284278474506240,130509259754593318496376665060,8107405596523654695095077175296,525358015896796804145274761270600

%N Column 1 of triangle A290580.

%C a(n) = A290580(n+2,1) for n>=1.

%H Vaclav Kotesovec, <a href="/A290581/b290581.txt">Table of n, a(n) for n = 1..75</a>

%F a(n) ~ c * n^(n+2), where c = (exp(5) - 4*exp(3) - exp(1))/16 = 4.0845455988354304513775733719295... - _Vaclav Kotesovec_, Aug 21 2017

%o (PARI) /* As column 1 of triangle A290580 */

%o { A290580(n,k) = my(W=1,E=1, S=x,C=1,D=1); for(i=0,n,

%o S = intformal(C*D +x*O(x^n)) ;

%o C = 1 - intformal(S*D) ; D = 1 - m*intformal(S*C) ;

%o E = subst( (1 + S)/C,m,1-m) ) ;

%o for(i=0,n, W = subst(E,x,x*W));

%o n!*polcoeff(polcoeff(W, n,x), k,m) }

%o for(n=1,25, print1( A290580(n+2,1), ", "))

%Y Cf. A290580, A291214.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Aug 07 2017