A355086
E.g.f. A(x) satisfies A(x) = 1 - log(1-x) * A(2*x).
Original entry on oeis.org
1, 1, 5, 68, 2318, 191364, 37322176, 16851654336, 17323677619888, 39991811695203552, 204958165376127918144, 2309776412016044230960128, 56778926016923229432156258048, 3023733345610004146919028796718592
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, 2^(i-j)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
A367830
E.g.f. A(x) satisfies A(x) = (1 + (exp(x) - 1) * A(2*x)) / (1 - x).
Original entry on oeis.org
1, 2, 13, 208, 7817, 681626, 136872113, 62739300968, 64993463748977, 150619722938940622, 773428868899900772345, 8724654696222415759129388, 214574098061440421518595200025, 11429824974654804201081062775335234, 1311103770238649103823410558613476172193
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 2^(i-j)*binomial(i, j)*v[i-j+1])); v;
A352859
a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k+1) * 2^k * a(k).
Original entry on oeis.org
1, 1, 4, 25, 280, 5665, 211516, 14907673, 2021820016, 535262714881, 279317901141172, 289064917007756761, 595455410823115765768, 2446703815513439818406305, 20077597428602000393057306476, 329252263598282049972950683567705, 10794203801863458962317873561872563680
Offset: 0
-
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k + 1] 2^k a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; A[] = 0; Do[A[x] = 1 + x A[2 x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
A355084
E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(2*x).
Original entry on oeis.org
1, 1, 3, 32, 962, 74604, 14102416, 6268777248, 6394217598800, 14703540690658848, 75208658403123879744, 846736815151560907880448, 20804324374762392749905814784, 1107653447201119751335031683041792, 127026805293926861783650032004892737536
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^(j-1)*2^(i-j)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
A355088
E.g.f. A(x) satisfies A(x) = 1 + (exp(x) - 1) * A(3*x).
Original entry on oeis.org
1, 1, 7, 199, 21883, 8916991, 13027669147, 66525761289919, 1164200761777844203, 68750129286493392353311, 13532431689375421261723713787, 8789916574829303798007959322784639, 18685340957126032386127459367999667264523
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, 3^j*binomial(i, j)*v[j+1])); v;
A355122
E.g.f. A(x) satisfies A(x) = 1 + (exp(x) - 1) * A(2 * (exp(x) - 1)).
Original entry on oeis.org
1, 1, 5, 73, 2725, 242921, 50068197, 23441365641, 24644653272869, 57655911504114985, 297771560486880287589, 3370400630994211122517705, 83052841013576647141181337509, 4428866659075152490151174819022697, 508340576698412171558866359984025695205
Offset: 0
-
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*2^(j-1)*stirling(i, j, 2)*v[j])); v;
A355232
E.g.f. A(x) satisfies A'(x) = 1 + (exp(x) - 1) * A(2*x).
Original entry on oeis.org
0, 1, 0, 4, 6, 136, 810, 28204, 458766, 30584656, 1191878610, 162323643604, 14307180186486, 4073323890279736, 788119370902131450, 472616432593062958204, 197219048399199774543966, 249355424516977575240738976
Offset: 0
-
a_vector(n) = my(v=vector(n)); v[1]=1; for(i=1, n-1, v[i+1]=sum(j=1, i-1, 2^j*binomial(i, j)*v[j])); concat(0, v);
A355109
a(n) = 1 + Sum_{k=1..n-1} binomial(n-1,k) * 2^(k-1) * a(k).
Original entry on oeis.org
1, 1, 2, 7, 44, 493, 9974, 372403, 26247008, 3559692121, 942403603562, 491777568765151, 508938530329020692, 1048381120745440503877, 4307758467916752367544414, 35349370769806113877653011083, 579693879415731511179957972407624
Offset: 0
-
a:= proc(n) option remember; 1+add(a(k)*
binomial(n-1, k)*2^(k-1), k=1..n-1)
end:
seq(a(n), n=0..16); # Alois P. Heinz, Jun 19 2022
-
a[n_] := a[n] = 1 + Sum[Binomial[n - 1, k] 2^(k - 1) a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; A[] = 0; Do[A[x] = (2 - x + x A[2 x/(1 - x)])/(2 (1 - x)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Showing 1-8 of 8 results.