A329754 - OEIS

A329754

Doubly pentagonal pyramidal numbers.

0, 1, 126, 3078, 32800, 213750, 1008126, 3783976, 11985408, 33297075, 83338750, 191592126, 410450976, 828497488, 1589341950, 2917620000, 5154021376, 8801526501, 14585352318, 23529456550, 37052820000, 57089119626, 86233820926, 127923156648, 186649920000, 268221484375, 380065968126

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..26.

Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

G.f.: x*(1 + 116*x + 1863*x^2 + 7570*x^3 + 9350*x^4 + 3474*x^5 + 304*x^6 + 2*x^7)/(1 - x)^10.

a(n) = A002411(A002411(n)).

a(n) = Sum_{k=0..A002411(n)} A000326(k).

a(n) = n^4 *(n^3+n^2+2) *(n+1)^2 /16. - R. J. Mathar, Nov 28 2019

MATHEMATICA

A002411[n_] := n^2 (n + 1)/2; a[n_] := A002411[A002411[n]]; Table[a[n], {n, 0, 26}]

Table[Sum[k (3 k - 1)/2, {k, 0, n^2 (n + 1)/2}], {n, 0, 26}]

nmax = 26; CoefficientList[Series[x (1 + 116 x + 1863 x^2 + 7570 x^3 + 9350 x^4 + 3474 x^5 + 304 x^6 + 2 x^7)/(1 - x)^10, {x, 0, nmax}], x]

LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 126, 3078, 32800, 213750, 1008126, 3783976, 11985408, 33297075}, 27]

CROSSREFS

Cf. A000326, A002411, A140236, A232713, A329753, A329755, A329756, A329757.

Sequence in context: A113857 A267282 A008397 * A202593 A293104 A267750

Adjacent sequences: A329751 A329752 A329753 * A329755 A329756 A329757

KEYWORD

nonn,easy

AUTHOR

Ilya Gutkovskiy, Nov 20 2019

STATUS

approved