A006173 -id:A006173 - cp's OEIS frontend

A006177 Witt vector *2!/2!.

1, 1, 3, 8, 25, 72, 245, 772, 2692, 8925, 32065, 109890, 400023, 1402723, 5165327, 18484746, 68635477, 248339122, 930138521, 3406231198, 12810761323, 47306348881, 178987624513, 665627041157, 2528210175630, 9456885664122

Offset: 1

Simon Plouffe

nonn

The Somos transform sends sequence {a(n)} to sequence with g.f. Product_{i=1..n} 1/(1-a(i)*x^i).

If c is the Witt transform of b then b(n) = Sum_{d|n} A074650(n/d, c(d)).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-108.
H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-107. (Annotated scanned copy)

Cf. A006173, A006973.

Inverse Somos transform of A000108. - Wouter Meeussen, Aug 20 2002

Witt transform of A022553.

Edited by Christian G. Bower, Aug 20 2002, Aug 28 2002

A006174 Witt vector *3!.

Original entry on oeis.org

6, 27, 488, 7974, 149796, 2725447, 56970432, 1151053821, 25279412332, 543871341927, 12411512060544, 278163517356594, 6498314231705568, 149846653983570795, 3565206002960088128, 84045618111578025105

Offset: 1

Simon Plouffe

nonn

If c is the Witt transform of b then b(n) = Sum_{d|n} A074650(n/d, c(d)).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-108.
H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-107. (Annotated scanned copy)

Witt transform of A074651.

More terms and formula from Christian G. Bower, Aug 28 2002

A006175 Witt vector *4!.

Original entry on oeis.org

24, 972, 118592, 15210414, 2344956480, 377420590432, 67501965869568, 12329221295657241, 2383082885396731968, 467786496795764717088, 95188347941581635319296, 19578329367376510676884584

Offset: 1

Simon Plouffe

nonn

If c is the Witt transform of b then b(n) = Sum_{d|n} A074650(n/d, c(d)).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-108.
H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-107. (Annotated scanned copy)

Witt transform of A074652.

More terms and formula from Christian G. Bower, Aug 28 2002

A006176 Witt vector *5!.

Original entry on oeis.org

120, 49500, 55480000, 75108093750, 124667171985024, 226899085942554400, 453922674315047424000, 954267187464733528198125, 2112236210012497151219800000, 4825706564405954731805322783552

Offset: 1

Simon Plouffe

nonn

If c is the Witt transform of b then b(n) = Sum_{d|n} A074650(n/d, c(d)).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-108.
H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-107. (Annotated scanned copy)

Witt transform of A074653.

More terms and formula from Christian G. Bower, Aug 28 2002

A006178 Witt vector *3!/3!.

Original entry on oeis.org

1, 7, 93, 1419, 25225, 472037, 9501737, 196190781, 4219610242, 92198459515, 2068590840349, 46897782768404, 1083052539395723, 25199771186287195, 594383312662808405, 14098935496013599680, 337939791145403719897

Offset: 1

Simon Plouffe

nonn

If c is the Witt transform of b then b(n) = Sum_{d|n} A074650(n/d, c(d)).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-108.
H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-107. (Annotated scanned copy)

Witt transform of A029808.

More terms and formula from Christian G. Bower, Aug 28 2002

A006179 Witt vector *4!/4!.

Original entry on oeis.org

1, 52, 5133, 655554, 97772875, 16019720210, 2812609211657, 518332479161091, 99318252448110232, 19600890528520952329, 3966181169996511862429, 818653886943854653597621, 171938262068874336023196923

Offset: 1

Simon Plouffe

nonn

If c is the Witt transform of b then b(n) = Sum_{d|n} A074650(n/d, c(d)).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-108.
H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-107. (Annotated scanned copy)

Witt transform of A029809.

More terms and formula from Christian G. Bower, Aug 28 2002

A006180 Witt vector *5!/5!.

Original entry on oeis.org

1, 472, 467133, 636430764, 1038934571875, 1903882757758426, 3782689379194538057, 7975541699963490241566, 17602442746255160006062232, 40278440105728693363331297293

Offset: 1

Simon Plouffe

nonn

If c is the Witt transform of b then b(n) = Sum_{d|n} A074650(n/d, c(d)).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-108.
H. Gaudier, Relèvement des coefficients binomiaux dans les vecteurs de Witt, Séminaire Lotharingien de Combinatoire. Institut de Recherche Math. Avancée, Université Louis Pasteur, Strasbourg, Actes 16 (1988), 358/S-18, pp. 93-107. (Annotated scanned copy)

Witt transform of A074654.

More terms and formula from Christian G. Bower, Aug 28 2002

A061655 The number 2 (that is, 1+1) in the Witt vector ring for p=2 over the integers.

Original entry on oeis.org

2, -1, -4, -40, -4960, -147166720, -299211527038566400, -2703337074029927682081937523621232640

Offset: 0

David A. Madore, Jun 15 2001

sign

			a(0)^4 + 2*a(1)^2 + 4*a(2) = 2^4 + 2*(-1)^2 + 4*(-4) = 16+2-16 = 2.

Jean-Pierre Serre, Local Fields (Corps Locaux), chapter 2, paragraph 6

Cf. A006173 and others.

Sum(2^j*a(j)^(2^(i-j)), j=0..i)=2 for all i.

cp's OEIS Frontend

A006177 Witt vector *2!/2!.

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A006174 Witt vector *3!.

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A006175 Witt vector *4!.

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A006176 Witt vector *5!.

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A006178 Witt vector *3!/3!.

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A006179 Witt vector *4!/4!.

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A006180 Witt vector *5!/5!.

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A061655 The number 2 (that is, 1+1) in the Witt vector ring for p=2 over the integers.

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