A337597
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * 6^(k-1) * a(n-k).
Original entry on oeis.org
1, 1, 8, 96, 1896, 55416, 2182752, 111162528, 7088997888, 550749341952, 51058009732608, 5556160183592448, 699989463219105792, 100917906076208203776, 16486415052067886690304, 3026039346413717945757696, 619431153899977856767131648, 140491838894751995366936641536, 35102748598142373142198776889344
Offset: 0
-
S:= series(exp((BesselI(0,2*sqrt(6*x))-1)/6),x,51):
seq(coeff(S,x,j)*(j!)^2, j=0..50); # Robert Israel, Sep 06 2020
-
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k 6^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[(BesselI[0, 2 Sqrt[6 x]] - 1)/6], {x, 0, nmax}], x] Range[0, nmax]!^2
A337592
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * 2^(k-1) * a(n-k).
Original entry on oeis.org
1, 1, 4, 28, 312, 4936, 104128, 2806336, 93560064, 3765265408, 179415074304, 9964625629696, 636737424291840, 46303081167540224, 3796275000959266816, 348100339275620651008, 35448445862069986361344, 3984266642444252234153984, 491556877841462376382332928
Offset: 0
-
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k 2^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[(BesselI[0, 2 Sqrt[2 x]] - 1)/2], {x, 0, nmax}], x] Range[0, nmax]!^2
A337594
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * 4^(k-1) * a(n-k).
Original entry on oeis.org
1, 1, 6, 58, 920, 21176, 654960, 26114768, 1298070912, 78359732608, 5630565514496, 473796572027648, 46060380961356800, 5114737212582603776, 642502387594286036992, 90542358999393528670208, 14209873001490130067095552, 2467784343879850163370295296, 471558856613839054976849608704
Offset: 0
-
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k 4^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[(BesselI[0, 4 Sqrt[x]] - 1)/4], {x, 0, nmax}], x] Range[0, nmax]!^2
A337595
a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * 5^(k-1) * a(n-k).
Original entry on oeis.org
1, 1, 7, 76, 1359, 35620, 1256470, 57247765, 3259660095, 225795951580, 18644190437550, 1805220546542425, 202173130530484350, 25889773647793362425, 3754040522961719322325, 611181508958872398483625, 110903705593861290502897375, 22285223101687304853202923500, 4930523789420612133816212731750
Offset: 0
-
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k 5^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[Exp[(BesselI[0, 2 Sqrt[5 x]] - 1)/5], {x, 0, nmax}], x] Range[0, nmax]!^2
A333982
a(0) = 0; a(n) = 3^(n-1) + (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * 3^(k-1) * (n-k) * a(n-k).
Original entry on oeis.org
0, 1, 5, 48, 909, 28836, 1371384, 91308708, 8106024861, 925225277004, 132007041682380, 23019553116101268, 4817014157800460664, 1191268407723761654964, 343706793228408937835772, 114423311913128119741898268, 43534429651349601213257298621, 18771927426013054800534345817884, 9106204442628918977341144456510260
Offset: 0
-
a[0] = 0; a[n_] := a[n] = 3^(n - 1) + (1/n) Sum[Binomial[n, k]^2 3^(k - 1) (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n],{n, 0, 18}]
nmax = 18; CoefficientList[Series[-Log[(4 - BesselI[0, 2 Sqrt[3 x]])/3], {x, 0, nmax}], x] Range[0, nmax]!^2
Showing 1-5 of 5 results.