A316083 -id:A316083 - cp's OEIS frontend

A316085 Product_{k>=1} 1/(1 - a(k)x^k) = Sum_{k>=0} (kx)^k.

1, 3, 23, 220, 2800, 42315, 763220, 15710280, 366711200, 9529898752, 273549419552, 8586085364211, 292755986184548, 10772558331396572, 425587704331945152, 17966093939959188380, 807152054953801845760, 38451298338305570267680

Offset: 1

Seiichi Manyama, Jun 23 2018

nonn

			1/((1-x)*(1-3*x^2)*(1-23*x^3)*(1-220*x^4)* ... ) = 1 + x + 4*x^2 + 27*x^3 + 256*x^4 + ... .

Seiichi Manyama, Table of n, a(n) for n = 1..386

Cf. A000312, A316083.

a(n) ~ n^n. - Vaclav Kotesovec, Jun 18 2019

A359265 Product_{n>=1} (1 + a(n) * x^n) = 1 + Sum_{n>=1} n^3 * x^n.

Original entry on oeis.org

1, 8, 19, 45, -72, -224, -72, 3465, 1656, -4752, -31248, -440, 62064, 415008, 936432, 6776793, -16454232, -24983784, 74804904, 468856296, 236519784, -2495390904, -8714625696, -8228470832, 62274531168, 155889061848, -47291852448, -1334769988176, -4304113760232

Offset: 1

Seiichi Manyama, Dec 28 2022

sign

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Cf. A000578, A147559, A147654, A316083.

S:= 1 + x*(x^2 + 4*x + 1)/(x - 1)^4:
for n from 1 to 30 do
  SS:= series(S,x,n+1);
  A[n]:= coeff(SS,x,n);
  S:= S/(1+A[n]*x^n);
od:
seq(A[i],i=1..30); # Robert Israel, Dec 28 2022

cp's OEIS Frontend

A316085 Product_{k>=1} 1/(1 - a(k)x^k) = Sum_{k>=0} (kx)^k.

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A359265 Product_{n>=1} (1 + a(n) * x^n) = 1 + Sum_{n>=1} n^3 * x^n.

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Author

Keywords

Links

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Maple

cp's OEIS Frontend

A316085 Product_{k>=1} 1/(1 - a(k)*x^k) = Sum_{k>=0} (k*x)^k.

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Author

Keywords

Examples

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Formula

A359265 Product_{n>=1} (1 + a(n) * x^n) = 1 + Sum_{n>=1} n^3 * x^n.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

A316085 Product_{k>=1} 1/(1 - a(k)x^k) = Sum_{k>=0} (kx)^k.