cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 11 results. Next

A171200 G.f. satisfies A(x) = 1 + x*A(2x)^3.

Original entry on oeis.org

1, 1, 6, 84, 2312, 121056, 12173568, 2391143424, 928316362752, 716762538541056, 1103851068987015168, 3395472896229407981568, 20875407961847891162038272, 256600638160251032545689337856, 6307244441266548036155317187248128
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Links

Crossrefs

Cf. A135867, A171201, A171202-A171211, A343439.

Programs

  • Mathematica
    m = 15; A[] = 0; Do[A[x] = 1 + x A[2x]^3 + O[x]^m // Normal, {m}];
CoefficientList[A[x], x] (* Jean-François Alcover, Nov 07 2019 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^3); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{i=0..n-1} Sum_{j=0..n-i-1} a(i) * a(j) * a(n-i-j-1). - Ilya Gutkovskiy, Nov 03 2021

A171202 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^4.

Original entry on oeis.org

1, 1, 8, 152, 5664, 399376, 53846016, 14141384704, 7330134466560, 7551251740344320, 15510852680588984320, 63626087316632048238592, 521607805205244557347782656, 8549156556447111748331767857152, 280190094729160875643888549840814080, 18364219805837823940403573170370661842944
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Links

Crossrefs

Cf. A135867, A171200, A171201, A171203, A171204-A171211, A343439.
Cf. A143047, A171193.

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = 1 + x*A[2x]^4 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^4); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{i, j, k, l>=0 and i+j+k+l=n-1} a(i) * a(j) * a(k) * a(l). - Seiichi Manyama, Jul 08 2025

A171204 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^5.

Original entry on oeis.org

1, 1, 10, 240, 11280, 1000080, 169100832, 55605632640, 36058105605120, 46450803286978560, 119290436529298554880, 611727201854914747760640, 6268994998754867059071385600, 128439243721180540266999017635840, 5261899692949082390205726962630000640, 431096933496167311430326245852780460769280
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Links

Crossrefs

Cf. A135867, A171200-A171203, A171205, A171206-A171211, A343439.
Cf. A143048, A171194.

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = 1 + x*A[2x]^5 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^5); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{i, j, k, l, m>=0 and i+j+k+l+m=n-1} a(i) * a(j) * a(k) * a(l) * a(m). - Seiichi Manyama, Jul 08 2025

A171206 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^6.

Original entry on oeis.org

1, 1, 12, 348, 19744, 2108784, 428817600, 169398274624, 131889504749568, 203937600707475456, 628561895904796999680, 3868208404121906515820544, 47571342639450113377565933568, 1169589733863427138021074362433536, 57499379103783344787572704263568097280, 5652994168279651703590653986228287051923456
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Links

Crossrefs

Cf. A135867, A171200-A171205, A171207, A171208-A171211, A343439.
Cf. A143049, A171195.

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = 1+x*A[2x]^6 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^6); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_6>=0 and x_1+x_2+...+x_6=n-1} Product_{k=1..6} a(x_k). - Seiichi Manyama, Jul 08 2025

A171208 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^7.

Original entry on oeis.org

1, 1, 14, 476, 31640, 3953488, 939383200, 433281169216, 393718899904640, 710399428248892928, 2554705943898166145024, 18342976469146094416494592, 263185684727811758287894478848, 7549222852919288301041224694890496, 432993292623369448352459156263293419520
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Links

Crossrefs

Cf. A135867, A171200-A171207, A171209, A171210-A171211, A343439.
Cf. A171196.

Programs

  • Mathematica
    terms = 15; A[] = 0; Do[A[x] = 1+x*A[2x]^7 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^7); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_7>=0 and x_1+x_2+...+x_7=n-1} Product_{k=1..7} a(x_k). - Seiichi Manyama, Jul 08 2025

A171210 G.f. A(x) satisfies A(x) = 1 + x*A(2*x)^8.

Original entry on oeis.org

1, 1, 16, 624, 47552, 6804576, 1849952000, 975746615040, 1013611906401280, 2090459909088346368, 8592166589474459877376, 70508055994868618069409792, 1156194054760373598022278840320, 37902377449956182566891283844956160, 2484501232375923934830943089632156319744
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Links

Crossrefs

Cf. A135867, A171200-A171209, A171211, A343439.
Cf. A171197.

Programs

  • Mathematica
    terms = 15; A[] = 0; Do[A[x] = 1+x*A[2x]^8 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^8); polcoeff(A, n)}

Formula

a(0) = 1; a(n) = 2^(n-1) * Sum_{x_1, x_2, ..., x_8>=0 and x_1+x_2+...+x_8=n-1} Product_{k=1..8} a(x_k). - Seiichi Manyama, Jul 08 2025

A171201 G.f. satisfies: A(x) = (1 + x*A(2x))^3.

Original entry on oeis.org

1, 3, 21, 289, 7566, 380424, 37361616, 7252471584, 2799853666176, 2155959119115264, 3315891500224031232, 10193070293871040606464, 62646640175842537242599936, 769927299959295414569740867584, 18923273743619678311418282019397632, 930154604531789703005691292148132511744
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Cf. A135868, A171200, A171202-A171211.

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = (1 + x*A[2x])^3 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=(1+x*subst(A, x, 2*x))^3); polcoeff(A, n)}

Formula

Self-convolution cube of A171200 where a(n) = A171200(n+1)/2^n for n>=0.

Extensions

a(14)-a(15) from Stefano Spezia, Apr 02 2025

A171203 G.f. satisfies: A(x) = (1 + x*A(2x))^4.

Original entry on oeis.org

1, 4, 38, 708, 24961, 1682688, 220959136, 57266675520, 29497077110720, 30294634141775360, 62134850895148484608, 254691311135373319017472, 2087196424913845641682560512, 34202892422993270952623113994240, 1120863025258656246362522776511881216, 73460242428855296330451249854756580540416
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Cf. A135868, A171200, A171201, A171202, A171204-A171211.

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = (1 + x*A[2x])^4 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=(1+x*subst(A, x, 2*x))^4); polcoeff(A, n)}

Formula

Self-convolution 4th power of A171202 where a(n) = A171202(n+1)/2^n for n>=0.

Extensions

a(14)-a(15) from Stefano Spezia, Apr 02 2025

A171205 G.f. satisfies: A(x) = (1 + x*A(2x))^5.

Original entry on oeis.org

1, 5, 60, 1410, 62505, 5284401, 868838010, 281703950040, 181448450339760, 232989133846286240, 597389845561440183360, 3061032714235774931187200, 31357237236616342838622807040, 642321739861948533960660029617920, 26312068694834430629292373404100369920, 2155589935049851254662487477552439610480640
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Cf. A135868, A171200-A171203, A171204, A171206-A171211.

Programs

  • Mathematica
    terms = 16; A[] = 0; Do[A[x] = (1 + x*A[2x])^5 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=(1+x*subst(A, x, 2*x))^5); polcoeff(A, n)}

Formula

Self-convolution 5th power of A171204 where a(n) = A171204(n+1)/2^n for n>=0.

Extensions

a(14)-a(15) from Stefano Spezia, Apr 02 2025

A171207 G.f. satisfies: A(x) = (1 + x*A(2x))^6.

Original entry on oeis.org

1, 6, 87, 2468, 131799, 13400550, 2646848041, 1030386755856, 796631252763576, 1227659952939056640, 3777547269650299331856, 23228194648169000672639616, 285544368619000766118426358016, 7018967175754802830514246125923840, 345031382341287335424234252089128848384
Offset: 0

Views

Author

Paul D. Hanna, Dec 05 2009

Keywords

Crossrefs

Cf. A135868, A171200-A171205, A171206, A171208-A171211.

Programs

  • Mathematica
    terms = 15; A[] = 0; Do[A[x] = (1+x*A[2x])^6 + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2025 *)
  • PARI
    {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=(1+x*subst(A, x, 2*x))^6); polcoeff(A, n)}

Formula

Self-convolution 6th power of A171206 where a(n) = A171206(n+1)/2^n for n>=0.

Extensions

a(14) from Stefano Spezia, Apr 02 2025
Showing 1-10 of 11 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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