A377790 -id:A377790 - cp's OEIS frontend

A377789 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - 2*log(1-x)) ).

1, 2, 10, 88, 1148, 20088, 442896, 11802096, 369132256, 13261156416, 538227938880, 24359100451200, 1216403663398656, 66440221207025664, 3940468338389603328, 252190997066643909120, 17324237625466992906240, 1271459220768570290626560, 99289436336361780797288448

Offset: 0

Seiichi Manyama, Nov 07 2024

nonn

Index entries for reversions of series

Cf. A138013, A377790.

Cf. A370941, A371005.

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1-2*log(1-x)))/x))

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

a(n) = n! * Sum_{k=0..n} 2^k * |Stirling1(n,k)|/(n-k+1)!.

A377803 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - log(1-3*x) / 3) ).

Original entry on oeis.org

1, 1, 5, 51, 798, 16914, 453294, 14704542, 560274336, 24529661568, 1213557885720, 66956662956600, 4076440417367856, 271472012197547472, 19631093304600307152, 1531919987372848152240, 128314172533501646058240, 11482569303348317402868480, 1093343670892117401737893632

Offset: 0

Seiichi Manyama, Nov 08 2024

nonn

Index entries for reversions of series

Cf. A138013, A377737.

Cf. A352069, A370907, A370939, A377790.

my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1-log(1-3*x)/3))/x))

a(n) = n!*sum(k=0, n, 3^(n-k)*abs(stirling(n, k, 1))/(n-k+1)!);

a(n) = n! * Sum_{k=0..n} 3^(n-k) * |Stirling1(n,k)|/(n-k+1)!.

cp's OEIS Frontend

A377789 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - 2*log(1-x)) ).

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A377803 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 - log(1-3*x) / 3) ).

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Author

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PARI

PARI

Formula