A200542 - OEIS

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A200542

E.g.f. A(x) satisfies differential equation A'''(x)=A(x)+1/2*A(x)^2, A(0)=0, A'(0)=1, A''(0)=1, A'''(0)=1.

1, 1, 1, 1, 2, 4, 8, 17, 41, 113, 340, 1070, 3592, 12979, 50107, 204325, 875702, 3947560, 18724328, 93137201, 484066913, 2623523381, 14811843184, 87000588266, 530736806728

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OFFSET

1,5

LINKS

Table of n, a(n) for n=1..25.

FORMULA

a(n)=n!*b(n), b(n)=1/(n*(n-1)*(n-2))*(i=1..n-4, b(n-3)+1/2*sum(b(i)*b(n-3-i))), n>3, b(1)=1, b(2)=1/2, b(3)=1/6.

PROG

(Maxima)

a(n):=if n<4 then 1/n! else 1/(n*(n-1)*(n-2))*(a(n-3)+1/2*sum(a(i)*a(n-3-i), i, 1, n-4));

makelist(n!*a(n), n, 1, 25);

CROSSREFS

Sequence in context: A331686 A373632 A156805 * A272105 A367114 A283162

Adjacent sequences: A200539 A200540 A200541 * A200543 A200544 A200545

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Nov 18 2011

STATUS

approved