A113670
Self-convolution 4th power equals A113664, where a(n) = n*A113664(n-1) for n>=1, with a(0)=1.
Original entry on oeis.org
1, 1, 8, 114, 2224, 53725, 1528200, 49703108, 1813503712, 73247619060, 3242579748000, 156107189374202, 8121266448765936, 454110696002834806, 27165980379205109232, 1731608155057922555400, 117183510733473232477120
Offset: 0
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{a(n)=local(A=1+x*O(x^n));for(i=1,n, A=1+x*deriv(x*A^4));polcoeff(A,n,x)}
A113663
Self-convolution cube of A113669, where a(n) = A113669(n+1)/(n+1).
Original entry on oeis.org
1, 3, 21, 226, 3216, 56229, 1158249, 27367560, 728245038, 21531918486, 700096811670, 24826071871890, 953594302010230, 39446976470619801, 1748616265593936681, 82701936091459565976, 4157268410857737364182
Offset: 0
-
{a(n)=local(A=1+x*O(x^n));for(i=1,n, A=(1+x*deriv(x*A))^3);polcoeff(A,n,x)}
A113665
Self-convolution 5th power of A113671, where a(n) = A113671(n+1)/(n+1).
Original entry on oeis.org
1, 5, 60, 1110, 27105, 811026, 28511130, 1146762120, 51826136580, 2597311722545, 142897603735880, 8561763675801900, 554962861232408910, 38698651781787343980, 2889100726488051970230, 229948324353525499175160
Offset: 0
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{a(n)=local(A=1+x*O(x^n));for(i=1,n, A=(1+x*deriv(x*A))^5);polcoeff(A,n,x)}
A113666
Self-convolution 6th power of A113672, where a(n) = A113672(n+1)/(n+1).
Original entry on oeis.org
1, 6, 87, 1946, 57429, 2075376, 88058362, 4272270786, 232769956974, 14056832143770, 931523802358452, 67202173618455120, 5243275012537211083, 439986956480236610424, 39519795153012732250740
Offset: 0
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{a(n)=local(A=1+x*O(x^n));for(i=1,n, A=(1+x*deriv(x*A))^6);polcoeff(A,n,x)}
A113667
Self-convolution 7th power of A113673, where a(n) = A113673(n+1)/(n+1).
Original entry on oeis.org
1, 7, 119, 3122, 108031, 4575543, 227428166, 12920344256, 823981508700, 58224680389435, 4513525625433076, 380801193456921958, 34738963053424196609, 3407790141561016562022, 357764735284328750251272
Offset: 0
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{a(n)=local(A=1+x*O(x^n));for(i=1,n, A=(1+x*deriv(x*A))^7);polcoeff(A,n,x)}
A113668
Self-convolution 8th power of A113674, where a(n) = A113674(n+1)/(n+1).
Original entry on oeis.org
1, 8, 156, 4696, 186406, 9053640, 515875660, 33585910968, 2453913830097, 198609146859416, 17630476159933080, 1703025192274201272, 177846105338917975896, 19968484152350242447288
Offset: 0
-
{a(n)=local(A=1+x*O(x^n));for(i=1,n, A=(1+x*deriv(x*A))^8);polcoeff(A,n,x)}
A113662
G.f. satisfies: A(x) = (1 + x*(d/dx x*A(x)) )^2.
Original entry on oeis.org
1, 2, 9, 62, 566, 6372, 84837, 1300214, 22511322, 434226300, 9231983850, 214481625516, 5406323440492, 146963638311880, 4286068830850797, 133501081493969574, 4423404073559930162, 155359770700317171084
Offset: 0
G.f. A(x) = 1 + 2*x + 9*x^2 + 62*x^3 + 566*x^4 + 6372*x^5 + 84837*x^6 + 1300214*x^7 + ...
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{a(n)=local(A=1+x*O(x^n));for(i=1,n, A=(1+x*deriv(x*A))^2);polcoeff(A,n,x)}
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A000699_seq(N) = {
my(a = vector(N)); a[1] = 1;
for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
};
Vec(sqr(Ser(A000699_seq(N)))) \\ Gheorghe Coserea, Jan 23 2017
Name replaced with an existing formula by
Paul D. Hanna, Sep 16 2024
A338377
G.f. satisfies: A(x) = (1 + x * d/dx(x*A(x)) )^n.
Original entry on oeis.org
1, 1, 9, 226, 10745, 811026, 88058362, 12920344256, 2453913830097, 584608650175630, 170543970449421371, 59769169004510011674, 24775053368568412720967, 11989194513429991057937296, 6698670769128767044654361520, 4280089524780608663200103685056, 3101341801862271814724389007080481
Offset: 0
a(2) = A113662(2) = 9
a(3) = A113663(3) = 226
a(4) = A113664(4) = 10745
a(5) = A113665(5) = 811026
a(6) = A113666(6) = 88058362
a(7) = A113667(7) = 12920344256
a(8) = A113668(8) = 2453913830097
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{a(n)=local(A=1+x*O(x^n)); for(i=1, n, A=(1+x*deriv(x*A))^n); polcoeff(A, n, x)}
for(n=0, 20, print1(a(n), ", "))
Showing 1-8 of 8 results.
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