A380080 - OEIS

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A380080

Expansion of e.g.f. (1/x) * Series_Reversion( x / sqrt(1 + 2*x*exp(x)) ).

1, 1, 3, 15, 109, 1045, 12501, 179599, 3015657, 57988809, 1257058585, 30337358491, 806837271021, 23448335293981, 739379851041573, 25143044445680295, 917252832237053521, 35735484803144976145, 1480838869407287923569, 65038486139094829172275, 3017945328547452509505045

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

E.g.f. A(x) satisfies A(x) = sqrt( 1 + 2*x*A(x)*exp(x*A(x)) ).

a(n) = (n!/(n+1)) * Sum_{k=0..n} 2^k * k^(n-k) * binomial(n/2+1/2,k)/(n-k)!.

PROG

(PARI) a(n) = n!*sum(k=0, n, 2^k*k^(n-k)*binomial(n/2+1/2, k)/(n-k)!)/(n+1);

CROSSREFS

Cf. A161633, A380081.

Cf. A380050.

Sequence in context: A136221 A366180 A153305 * A110328 A217061 A054201

Adjacent sequences: A380077 A380078 A380079 * A380081 A380085 A380086

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jan 11 2025

STATUS

approved

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