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A377829
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x)/(1 + x)^2 ).
1
1, 3, 25, 364, 7713, 216216, 7568041, 318256800, 15644919681, 880848974080, 55912403743161, 3951344780946432, 307737594185310625, 26190457718737019904, 2418475248758250599625, 240846113359411822759936, 25731326615411044591298049, 2935802801104074173428531200
OFFSET
0,2
FORMULA
E.g.f. A(x) satisfies A(x) = (1 + x*A(x))^2 * exp(x * A(x)).
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n+2,n-k)/k!.
a(n) ~ (2*(1 + sqrt(2)))^(n + 1/2) * n^(n-1) / exp((2 - sqrt(2))*n + 1 - sqrt(2)). - Vaclav Kotesovec, Nov 09 2024
PROG
(PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(2*n+2, n-k)/k!);
CROSSREFS
Cf. A377827.
Sequence in context: A129506 A143139 A231637 * A295765 A380674 A012481
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 09 2024
STATUS
approved